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# Delfour, Michel

Emeritus Professor

Faculty of Arts and Science - Department of Mathematics and Statistics

### Affiliations

• Membre Centre de recherches mathématiques
• Membre CRM  Centre de recherches mathématiques

### Research area

Michel Delfour is a Guggenheim, Killam, and SIAM Fellow and was awarded the Urgel-Archambault Prize for Physics, Mathematics, and Engineering from ACFAS. His research interests are: optimization and design of shapes and geometries, analysis and control of ordinary, delay, and partial differential systems, control and stabilization of large space structures, numerical methods in differential equations and optimization. His recent interests include the frequency assignment methods to land mobiles, the modelling and control of thin and asymptotic shells, the design of endoprotheses in interventional cardiology, and the design of the dynamics of drug release. He is the author of 13 books and more than 175 papers.

He has been president of the Canadian Mathematical Society and has served on numerous Canadian granting and advisory committees, as well as on panels,  boards, and executive committees of international organizations. He has been a professional engineer (Ordre des Ingénieurs du Québec) since 1966 and has been involved in numerous consulting activities for Canadian organizations.

### Student supervision Expand allCollapse all

Three-Dimensional Model of the Release and Diffusion of Paclitaxel in the Stent-Polymer-Wall-Lumen System of a Blood Vessel Theses and supervised dissertations / 2018-08
Lamontagne, Steven
Abstract
Stents are used in interventional cardiology in order to keep a diseased vessel open. New stents are coated with a medicinal agent that prevents the early reclosing caused by the proliferation of smooth muscle cells (SMC). In order to obtain the desired release kinetics for the SMC-controlling drug during the required therapeutic period, the current strategy focuses on biphasic or possibly polyphasic release from blends of degradable polymers. BlanchetDelfour-Garon [7] introduced an ordinary differential equation with two parameters and Garon-Delfour [42] a partial differential equation with two parameters to model the release kinetics. The parameters are all obtained from experimental release curves of Lao et al. [60] for pure polymers and polymer blends under infinite sink conditions. They are practical tools to numerically and theoretically simulate the 3D drug release from a thin coating of polymer to the aggregated wall and lumen of the blood vessel in order to facilitate the design and evaluation of the coating. The primary objective of this research was to pass from the thin, flat midsurface coating to the thin coating of a realistic 3D stent with curved and complex surface. To begin, the linearly diffusive model (and the results) of Delfour-Garon-Longo [31] that were obtained for a vessel with flat surface were extended to the case of a vessel with curved surface by finding the appropriate boundary conditions. The resulting model was then analysed from the point of view of the dose and the normalised concentration. Secondly, the resulting boundary condition from the 3D partial differential equation of Garon-Delfour was introduced into the model. This second nonlinear model was then used to study the normalised concentration as a function of the thickness of the polymer and the diffusion constant of the surrounding medium

«Sur la figure des colonnes» de Lagrange revisité Theses and supervised dissertations / 2018-01
Huot-Chantal, Francis
Abstract
The column's bucking load problem was formulated by Lagrange around 1770. There were many solutions proposed, but all contained some errors. Lagrange himself claimed the solution had a straight cylinder section, which was found to be suboptimal later. False solutions were mainly caused by the non-differentiability of the problem. In 1992, Cox and Overton revisited the problem using Auchmuty's dual principle and Clarke's generalized gradient. They established the existence of a solution by only considering columns whose profile is bounded above and below by some positive constants. According to Egorov, Cox and Overton's a priori hypothesis excluded possibly degenerated column's profiles and, as a consequence, they cannot justify and claim the existence of solutions. In this Master's thesis, we will study the optimal shape/profile problem and look for all the available information without assuming the existence of a priori bounds. Firstly, we will study the discrete form of the problem which will allow us to restrict the problem in finite dimension and guarantee the existence. Nonetheless, the problem will still be non-differentiable as it will keep his important characteristics. Essentially, in both continuous and discrete versions, we want to maximize the first generalized eigenvalue under a constant volume constraint. Since the problem is Hadamard semidifferentiable, a necessary optimality condition can be obtained. But in this work we rather concentrated on including possibly degenerate profiles by enlarging the Sobolev space of inflections for the minimization problem. Those new "custom-made" spaces are better suited for our purpose but, at the same time, they introduce new mathematical challenges. The column's bucking load problem can be viewed as a generic problem of optimizing the least non-simple eigenvalue. Therefore, this work is relevant in a broader perspective for mathematical and numerical purposes.

Représentation et identification des hypersurfaces Theses and supervised dissertations / 2012-12
Choueib, Hassan
Abstract
The mid-term objective of this work is to explore some formulations of shape identification and surface recognition problems from point measurements. Those problems have important applications in medical imaging, biometrics, security of the automatic access, and in the identification of Lagrangian Coherent Structures in Fluid Mechanics. For instance, the problem of identifying the different characteristics of the right hand or the face from a population to another or the follow-up after surgery from data generated by a scanner. The objective of this mémoire is to prepare the ground by reviewing the different mathematical tools available to apprehend the geometry as an identification or optimization variable. For surface identification it explores the use of distance functions, oriented distance functions, and level sets as in S. Osher and R. Fedkiw ; for surface recognition it emphasizes the construction of Courant metrics by A. M. Micheletti in 1972 and the point of view of R. Azencott and A. Trouvé in 1995 which consists in generating deformations of a reference surface via a family of diffeomorphisms. The accent will be put on the underlying mathematical foundations that it will attempt to clarify as necessary, and, if need be, on exploring new avenues.

Représentation et détection des images et des surfaces déformables Theses and supervised dissertations / 2011-08
Barolet, Justine C.
Abstract
The representation of a surface, its smoothing, and its use in identification, comparison, classification, and in the study of changes in volume, curvature, and topology are ubiquitous in the area of the scanning. Among mathematical methods, we have retained the diffeomorphisms of a reference pattern. There is a considerable interest, both theoretical and numerical, in approximating an arbitrary diffeomorphism by diffeomorphisms generated by velocity fields. On the theoretical front the question is : "is the subgroup of diffeomorphisms generated by velocity fields dense in Micheletti's larger group endowed with the Courant metric ?" In spite of some progress, the question remains open. The tracks followed have converged towards the subgroup of Lipschitzian diffeomorphisms of Azencott and Trouvé and its metric developed for imaging. It corresponds to a notion of geodesic between two diffeomorphisms in their subgroup. Optimization is then used to obtain a system of equations of the state adjoint state type characterizing the optimal solution of the identification problem from observations. This approach is adapted to the identification of surfaces obtained from a scanner such as, for instance, the scan of a face. This problem is much more difficult than the one of imaging. We introduce a curvilinear reference system and a faceted surface for numerical computations. We provide a formulation of the identification problem and of the computation of the change of volume from a reference scan.

Commande optimale et jeux différentiels linéaires quadratiques Theses and supervised dissertations / 2007
Dello Sbarba, Olivier
Abstract
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Les aspects mathématiques des stents enrobés Theses and supervised dissertations / 2006
Bourgeois, Étienne
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Représentations analytiques des objets géométriques et contours actifs en imagerie Theses and supervised dissertations / 2004
Dehaes, Mathieu
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Modélisation des stents en chirurgie cardiaque Theses and supervised dissertations / 2003
Longo, Vito
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

### Selected publications Expand allCollapse all

#### Introduction to optimization and Hadanard semi-differential calculus, deuxième édition

M. C. Delfour, Introduction to optimization and Hadanard semi-differential calculus, deuxième édition 27, xxi + 354 (2020), , SIAM-MOS, Society for Industrial and Applied Mathematics, Philadelphia, USA

#### On theTransfinite Mean Value Interpolation of Dicken and Floater

M. C. Delfour et A. Garon, On theTransfinite Mean Value Interpolation of Dicken and Floater 5, 1-11 (2020), , J. Pure and Applied Functional Analysis

#### Mesh adaptation based on transfinite mean value interpolation

A. Garon et M. C. Delfour, Mesh adaptation based on transfinite mean value interpolation , 1-35 (2020), https://doi.org/10.1016/j.jcp.2020.109248, J. of Computational Physics

#### "On the figure of columns" of Lagrange revisited

M. C. Delfour et F. Huot-Chantal, , "On the figure of columns" of Lagrange revisited 26, 855-876 (2019), , Journal of Convex Analysis

#### Three-Dimensional Drug Release in the Stent-Polymer-Wall-Lumen of a Blood Vessel

M.C. Delfour, A. Garon et S. Lamontagne, Three-Dimensional Drug Release in the Stent-Polymer-Wall-Lumen of a Blood Vessel 79, 1850-1871 (2019), , SIAM J. Appl. Math.

M. C. Delfour et A. Garon, Transfinite Interpolations for Free and Moving Boundary Problems 4, 765-801 (2019), , J. Pure and Applied Functional Analysis

#### Topological Derivative: a Semidifferential via the Minkowski Content

M. C. Delfour, Topological Derivative: a Semidifferential via the Minkowski Content 25, 957-982 (2018), , Journal of Convex Analysis

#### Control, Shape, and Topological Derivatives via Minimax Differentiability of Lagrangians

M. C. Delfour, Control, Shape, and Topological Derivatives via Minimax Differentiability of Lagrangians , 137-164 (2018), , dans "Numerical Methods for Optimal Control Problems," M. Falcone, R. Ferretti, L. Grüne, W. McEneaney, eds., Springer INdAM Series Vol. 29, Springer Nature Switzerland.

#### Parametric Semidifferentiability of Minimax of Lagrangians: Averaged Adjoint Approach

M. C. Delfour et K. Sturm, Parametric Semidifferentiability of Minimax of Lagrangians: Averaged Adjoint Approach 24, 1117-1142 (2017), , Journal of Convex Analysis

#### Differentials and Semidifferentials for Metric Spaces of Shapes and Geometries

M. C. Delfour, Differentials and Semidifferentials for Metric Spaces of Shapes and Geometries , 230-239 (2017), , dans ?System Modeling and Optimization, (CSMO 2015),'' L. Bociu, J. A. Desideri and A. Habbal, eds., AICT Series, Springer. (Proc. 27th IFIP TC7 Conference 2015, Sophia-Antipolis, France)

#### Metrics spaces of shapes and geometries from set parametrized functions

M. Delfour, Metrics spaces of shapes and geometries from set parametrized functions , 57-101 (2016), , dans "New trends in Shape Optimization," A. Pratelli and G. Leugering, eds, International Series of Numerical Mathematics, Birkhäuser Verlag.

#### Minimax differentiability via the averaged adjoint for control/shape sensitivity

M. C. Delfour et K. Sturm, Minimax differentiability via the averaged adjoint for control/shape sensitivity , 142-149 (2016), , Proceedings of the Second IFAC Workshop on Control of Systems Governed by Partial Differential Equations, IFAC-PaperOnLine 49-8

#### Arterial Stenosis: Hemodynamics and Drug Elutions, dans « PanVascular Medicine », 2nd ed., Peter Lanzer, ed.

M. Thiriet, M. C. Delfour et A. Garon, Arterial Stenosis: Hemodynamics and Drug Elutions, dans « PanVascular Medicine », 2nd ed., Peter Lanzer, ed. Volume 1, Part IV, Chapter 24, 781-868 (2015), , Springer Heidelberg New York Dordrecht London.

#### Metrics spaces of shapes and geometries from set parametrized functions

M. C. DELFOUR, Metrics spaces of shapes and geometries from set parametrized functions "New trends in Shape Optimization", A. Pratelli and G. Leugering, eds.,, 57-101 (2015), , International Series of Numerical Mathematics, Birkhäuser Verlag

A. Garon et M. C. Delfour, Three-dimensional quadratic model of paclitaxel release from biodegradable polymer films accepté le 24 juin 2014, 1-19 (2014), , SIAM J. Appl. Math.

#### Quadratic ODE and PDE models of drug release kinetics from biodegradable polymers

M. C. Delfour er A. Garon, Quadratic ODE and PDE models of drug release kinetics from biodegradable polymers , 13-24 (2013), , dans "25th IFIP TC7 Conference on System Modeling and Optimization", Dietmar Hömberg et Fredi Tröltzsch, eds, IFIP Adv. Inf. Commun. Technol., Springer, Berlin.

#### Introduction à l'optimisation et au calcul semi-différentiel

M. C. Delfour, Introduction à l'optimisation et au calcul semi-différentiel , (2012), , Collection: Sciences Sup., Mathématiques appliqués pour le Master/SMAI, Dunod, Paris. ISBN 978-2-10-057423-0.

#### Drug release kinetics from biodegradable polymers via partial differential equation models

M.C. Delfour, Drug release kinetics from biodegradable polymers via partial differential equation models 118, issue 1, , 161-183 (2012), , Acta Applicandae Mathematicae

#### Anisotropic mesh adaptation on Lagrangian Coherent Structures

P. Miron, J. Vétel, A. Garon, M. Delfour et Mouhammad El Hassan, Anisotropic mesh adaptation on Lagrangian Coherent Structures 231,, 6419-6437 (2012), , Journal of Computational Physics

#### Introduction to optimization and semi-differential calculus

M. C. Delfour, Introduction to optimization and semi-differential calculus , (2012), , série SIAM-MOS, Society for Industrial and Applied Mathematics, Philadelphia, USA. ISBN 978-1-611972-14-6.

#### Shapes and Geometries: Metrics, Analysis, Differential Calculus and Optimization

M.C. Delfour et J.-P. Zolésio, Shapes and Geometries: Metrics, Analysis, Differential Calculus and Optimization , (2011), , SIAM series on Advances in Design and Control, Society for Industrial and Applied Mathematics, Philadelphia, USA. ISBN 978-0-898719-36-9.

#### Quadratic models to fit experimental data of Paclitaxel release kinetics from biodegradable polymers

G. Blanchet, M.C. Delfour et A. Garon, Quadratic models to fit experimental data of Paclitaxel release kinetics from biodegradable polymers 71, No. 6, , 2269-2286 (2011), , SIAM J. Appl. Math. (Special Issue on Mathematical Modeling of Controlled Drug Delivery)

#### New equations for the dose under pulsative/periodic conditions in the design of coated stents

M.C. Delfour et A. Garon, New equations for the dose under pulsative/periodic conditions in the design of coated stents 13, No. 1, , 19-34 (2010), , Computer Methods in Biomechanics and Biomedical Engineering

#### Representations, composition, and decomposition of C1,1 hypersurfaces

M.C. Delfour, Representations, composition, and decomposition of C1,1 hypersurfaces , 85-104 (2009), , dans "Optimal control of coupled systems of partial differential equations", Internat. Ser. Numer. Math., 158, Birkhäuser Verlag, Basel.

M.C. Delfour et O. Dello Sbarba, Linear-quadratic differential games: closed loop saddle points 47, No. 6, , 3138-3166 (2009), , SIAM J. on Control and Optim.

#### Boundary smoothness of the solution of Maxwell's equations of electromagnetics

J.P. Zolésio et M.C. Delfour, Boundary smoothness of the solution of Maxwell's equations of electromagnetics , 492-506 (2009), , dans "System modeling and optimization", IFIP Adv. Inf. Commun. Technol., 312, Springer, Berlin.

#### Linear-Quadratic Differential Games: from finite to infinite dimension

M.C. Delfour, Linear-Quadratic Differential Games: from finite to infinite dimension 35, No. 4, , 431-446 (2008), , Applicationes Mathematicae

#### Representation of hypersurfaces and minimal smoothness of the midsurface in the theory of shells

M.C. Delfour, Representation of hypersurfaces and minimal smoothness of the midsurface in the theory of shells 37, No. 4, , 879-911 (2008), , Control and Cybernetics

#### General Patterns and Asymptotic Dose in the Design of Coated Stents

É. Bourgeois et M.C. Delfour, General Patterns and Asymptotic Dose in the Design of Coated Stents 11, issue 4, , 323-334 (2008), , Computer Methods in Biomechanics and Biomedical Engineering

#### Coupling Stokes and Darcy equations

J.M. Urquiza, D. N'dri, A. Garon, et M.C. Delfour, Coupling Stokes and Darcy equations 58, , 525-538 (2008), , Applied Numerical Mathematics

#### Jean-Paul Zolésio---a short biography

J. Sokolowski et M. C. Delfour, Jean-Paul Zolésio---a short biography 37, 743--745 (2008), , Control and Cybernetics

#### High Dimensional Partial Differential Equations in Science and Engineering

A.D. Bandrauk, M.C. Delfour, and C. Le Bris, High Dimensional Partial Differential Equations in Science and Engineering , (2007), , CRM Lecture Notes and Proceedings, vol 41, AMS Publ, R.I., ISBN-13 978-0-8218-3853-2.

#### Representation and Control of Infinite Dimensional Systems

A. Bensoussan, G. Da Prato, M.C. Delfour, and S.K. Mitter, Representation and Control of Infinite Dimensional Systems , (2007), , Birkhäuser Boston, Inc., Boston, Basel, Berlin.

M.C. Delfour, Linear-Quadratic Differential Games: Saddle Point and Riccati Differential Equation 46, No. 2, , 750-774 (2007), , SIAM J. Control and Optim.

#### Uniform Fat Segment and Cusp Properties for Compactness in Shape Optimization

M.C. Delfour, Uniform Fat Segment and Cusp Properties for Compactness in Shape Optimization 46, No. 2, , 385-419 (2007), , Appl Math Optim

#### Some New Results in Open and Closed-Loop Linear-Quadratic Differential Games

M.C. Delfour et O. Dello Sbarba , Some New Results in Open and Closed-Loop Linear-Quadratic Differential Games , 907-912 (2007), , dans "Proceedings 16th IEEE Mediterranean Conference on Control and Automation", IEEE Publications.

#### Shape and geometric methods in image processing

M. Dehaes et M.C. Delfour, Shape and geometric methods in image processing , 293-308 (2007), , dans "Free and moving boundaries analysis, simulation, and control", Lecture Notes in Pure and Applied Mathematics Volume 252, Chapman & Hall/CRC, Boca Raton, FL.

#### Evolution equations for shapes and geometries

M. C. Delfour et J.-P. Zolésio, Evolution equations for shapes and geometries 6, 399--417 (2006), , J. Evol. Equ.

#### A numerical study of primal mixed finite element approximations of Darcy equations

J. M. Urquiza, D. N'Dri, A. Garon et M. C. Delfour, A numerical study of primal mixed finite element approximations of Darcy equations 22, 901--915 (2006), , Comm. Numer. Methods Engrg.

#### Shape identification via metrics constructed from the oriented distance function

M. C. Delfour et J.-P. Zolésio, Shape identification via metrics constructed from the oriented distance function 34, 137--164 (2005), , Control Cybernet.

#### Modeling and design of coated stents to optimize the effect of the dose

M. C. Delfour, A. Garon et V. Longo, Modeling and design of coated stents to optimize the effect of the dose 65, 858--881 (electronic) (2005), , SIAM J. Appl. Math.

#### The uniform fat segment and cusp properties in shape optimization

M. C. Delfour, N. Doyon et J._P. Zolésio, The uniform fat segment and cusp properties in shape optimization , 85-96 (2005), , dans "Control and Boundary Analysis", J. Cagnol and J.-P. Zolésio, edsLect. Notes in Pure and Appl. Math. Vol. 240, Chapman & Hall/CRC, Boca Raton, FL.

#### Uniform cusp property, boundary integral, and compactness for shape optimization

M. C. Delfour, N. Doyon et J.-P. Zolésio, Uniform cusp property, boundary integral, and compactness for shape optimization , 25-40 (2005), , dans "System Modeling and Optimization", J. Cagnol and J.-P. Zolésio, eds, IFIP Int. Fed. Inf. Process., 166, Kluwer Acad. Publ., Boston, MA.

#### Extension of the uniform cusp property in shape optimization

M. C. Delfour, N. Doyon et J.-P. Zolésio, Extension of the uniform cusp property in shape optimization , 71-86 (2005), , dans "Control Theory of Partial Differential Equations", O. Emanuvilov, G. Leugering, R. Triggiani, and B. Zhang, eds, IFIP Int. Fed. Inf. Process., 166, Kluwer Acad. Publ., Boston, MA.

#### The new family of cracked sets and the image segmentation problem revisited

M. C. Delfour et J.-P. Zolésio, The new family of cracked sets and the image segmentation problem revisited 4, 29--52 (2004), , Commun. Inf. Syst.

#### Oriented distance function and its evolution equation for initial sets with thin boundary

M. C. Delfour et J.-P. Zolésio, Oriented distance function and its evolution equation for initial sets with thin boundary 42, 2286--2304 (electronic) (2004), , SIAM J. Control Optim.

#### Dynamical free boundary problem for an incompressible potential fluid flow in a time-varying domain

M. C. Delfour et J.-P. Zolésio, Dynamical free boundary problem for an incompressible potential fluid flow in a time-varying domain 12, 1--25 (2004), , J. Inverse Ill-Posed Probl.

#### Quantum Control: Mathematical and Numerical Challenges

A.D. Bandrauk, M.C. Delfour et C. Le Bris, Quantum Control: Mathematical and Numerical Challenges , (2003), , CRM Lecture Notes and Proceedings, vol 33, AMS Publ, R.I., ISBN 0-8218-3330-8.

#### Shapes and Geometries: Analysis, Differential Calculus and Optimization

M. C. Delfour et J.-P. Zolésio, Shapes and Geometries: Analysis, Differential Calculus and Optimization , (2001), , SIAM series on Advances in Design and Control, Society for Industrial and Applied Mathematics, Philadelphia, USA. ISBN 0-89871-489-3.

#### Characterization of the space of solutions of the membrane shell equation for arbitrary $C^{1,1}$ midsurfaces

M. C. Delfour, Characterization of the space of solutions of the membrane shell equation for arbitrary $C^{1,1}$ midsurfaces 28, 481--501 (1999), , Control Cybernet.

#### Fixed mesh approximation of ordinary differential equations with impulses

M. Delfour et F. Dubeau, Fixed mesh approximation of ordinary differential equations with impulses 78, 377--401 (1998), , Numer. Math.

#### Boundaries, interfaces and transitions

M. C. Delfour, Boundaries, interfaces and transitions , (1998), , CRM Proc. Lecture Notes Vol. 13, Amer. Math. Soc., Providence, RI. ISBN 0-8218-0505-3.

#### Error analysis of mixed finite elements for cylindrical shells

G. Yang, M. C. Delfour et M. Fortin, Error analysis of mixed finite elements for cylindrical shells 7, 261--277 (1997), , Adv. Comput. Math.

#### On the design and control of systems governed by differential equations on submanifolds

M. C. Delfour et J.-P. Zolésio, On the design and control of systems governed by differential equations on submanifolds 25, 497--514 (1996), , Control Cybernet.

#### Tangential differential equations for dynamical thin/shallow shells

Delfour, M. C. et Zolésio, J. P., Tangential differential equations for dynamical thin/shallow shells 128, 125--167 (1996), , J. Differential Equations

#### A boundary differential equation for thin shells

M. C. Delfour et J.-P. Zolésio, A boundary differential equation for thin shells 119, 426--449 (1995), , J. Differential Equations

#### One-sided derivative of minmax and saddle points with respect to a parameter

M. C. Delfour et J. Morgan, One-sided derivative of minmax and saddle points with respect to a parameter 31, 343--358 (1994), , Optimization

#### Shape analysis via oriented distance functions

M. C. Delfour et J.-P. Zolésio, Shape analysis via oriented distance functions 123, 129--201 (1994), , J. Funct. Anal.

#### Representation and Control of Infinite Dimensional Systems

A. Bensoussan, G. Da Prato, M.C. Delfour, et S.K. Mitter, Representation and Control of Infinite Dimensional Systems II, (1993), , Birkhäuser Boston, Inc., Boston, Basel, Berlin, ISBN 0-8176-3642-0, ISBN 3-7643-3642-0.

#### Noniterative approximations to the solution of the matrix Riccati differential equation

Delfour, M. C. et Ouansafi, A., Noniterative approximations to the solution of the matrix Riccati differential equation 29, 1648--1693 (1992), , SIAM J. Numer. Anal.

#### A complement to the differentiability of saddle points and min-max

M. C. Delfour et J. Morgan, A complement to the differentiability of saddle points and min-max 13, 87--94 (1992), , Optimal Control Appl. Methods

#### Optimal distribution of larvicide in running waters

Chalifour, Alain et Delfour, Michel C., Optimal distribution of larvicide in running waters 2, 264--303 (1992), , SIAM J. Optim.

#### Structure of shape derivatives for nonsmooth domains

M. C. Delfour et J.-P. Zolésio, Structure of shape derivatives for nonsmooth domains 104, 1--33 (1992), , J. Funct. Anal.

#### Unbounded solutions to the linear quadratic control problem

Da Prato, G. et Delfour, M. C., Unbounded solutions to the linear quadratic control problem 30, 31--48 (1992), , SIAM J. Control Optim.

#### Shape Optimization and Free Boundaries

M. C. Delfour et G. Sabidussi, Shape Optimization and Free Boundaries , (1992), , Series C: Mathematical and Physical Sciences, Vol 380, Kluwer Academic Publishers, Dordrecht, Boston, London. ISBN 0-7923-1944-3.

#### Representation and Control of Infinite Dimensional Systems

A. Bensoussan, G. Da Prato, M.C. Delfour, et S.K. Mitter, Representation and Control of Infinite Dimensional Systems I, (1992), , Birkhäuser Boston, Inc., Boston, Basel, Berlin. ISBN 0-8176-3641-2, ISBN 3-7643-3641-2.

#### Anatomy of the shape Hessian

M. C. Delfour et J.-P. Zolésio., Anatomy of the shape Hessian 159, 315--339 (1991), , Ann. Mat. Pura Appl. (4)

#### Velocity method and Lagrangian formulation for the computation of the shape Hessian

M. C. Delfour et J.-P. Zolésio, Velocity method and Lagrangian formulation for the computation of the shape Hessian 29, 1414--1442 (1991), , SIAM J. Control Optim.

#### Analyse des problèmes de forme par la dérivation des minimax

M. C. Delfour et J.-P. Zolésio, Analyse des problèmes de forme par la dérivation des minimax 6, 211--227 (1989), , Ann. Inst. H. Poincaré Anal. Non Linéaire

#### Shape sensitivity analysis via a penalization method

M. C. Delfour et J.-P. Zolésio, Shape sensitivity analysis via a penalization method 151, 179--212 (1988), , Ann. Mat. Pura Appl. (4)

#### Shape sensitivity analysis via min max differentiability

M. C. Delfour et J.-P. Zolésio, Shape sensitivity analysis via min max differentiability 26, 834--862 (1988), , SIAM J. Control Optim.

#### Approximation of nonlinear problems associated with radiating bodies in space

M. C. Delfour, G. Payre, G. et J.-P. Zolésio, Approximation of nonlinear problems associated with radiating bodies in space 24, 1077--1094 (1987), , SIAM J. Numer. Anal.

#### State space theory of linear time invariant systems with delays in state, control, and observation variables. I, II

Delfour, M. C. et Karrakchou, J., State space theory of linear time invariant systems with delays in state, control, and observation variables. I, II 125, 361--450 (1987), , J. Math. Anal. Appl.

#### Modeling, stabilization and control of serially connected beams

Chen, G., Delfour, M. C., Krall, A. M. et Payre, G., Modeling, stabilization and control of serially connected beams 25, 526--546 (1987), , SIAM J. Control Optim.

#### Stabilization of hyperbolic systems using concentrated sensors and actuators

Delfour, Michel C., Lagnese, John et Polis, Michael P., Stabilization of hyperbolic systems using concentrated sensors and actuators 31, 1091--1096 (1986), , IEEE Trans. Automat. Control

#### The linear-quadratic optimal control problem with delays in state and control variables: a state space approach

Delfour, M. C., The linear-quadratic optimal control problem with delays in state and control variables: a state space approach 24, 835--883 (1986), , SIAM J. Control Optim.

#### Dérivation d'un min max et application à la dérivation par rapport au contrôle d'une observation non différentiable de l'état

M. C. Delfour et J.-P. Zolésio, Dérivation d'un min max et application à la dérivation par rapport au contrôle d'une observation non différentiable de l'état 302, 571--574 (1986), , C. R. Acad. Sci. Paris Sér. I Math.

#### Discontinuous polynomial approximations in the theory of one-step, hybrid and multistep methods for nonlinear ordinary differential equations

Delfour, M. C. et Dubeau, F., Discontinuous polynomial approximations in the theory of one-step, hybrid and multistep methods for nonlinear ordinary differential equations 47, 169--189, S1--S8 (1986), , Math. Comp.

#### An optimal triangulation for second-order elliptic problems

M. C. Delfour, G. Payre et J.-P. Zolésio, An optimal triangulation for second-order elliptic problems 50, 231--261 (1985), , Comput. Methods Appl. Mech. Engrg.

#### Linear optimal control of systems with state and control variable delays

Delfour, M. C., Linear optimal control of systems with state and control variable delays 20, 69--77 (1984), , Automatica J. IFAC

#### Optimal design of minimum weight thermal diffuser with constraint on the output thermal power flux

M. C. Delfour, G. Payre et J.-P. Zolésio, Optimal design of minimum weight thermal diffuser with constraint on the output thermal power flux 9, 225--262 (1983), , Appl. Math. Optim.

#### Finite-difference solutions of a nonlinear Schrödinger equation

Delfour, M., Fortin, M. et Payre, G., Finite-difference solutions of a nonlinear Schrödinger equation 44, 277--288 (1981), , J. Comput. Phys.

#### Discontinuous Galerkin methods for ordinary differential equations

Delfour, M., Hager, W. et Trochu, F., Discontinuous Galerkin methods for ordinary differential equations 36, 455--473 (1981), , Math. Comp.

#### The structural operator $F$ and its role in the theory of retarded systems. II

Delfour, M. C. et Manitius, A., The structural operator $F$ and its role in the theory of retarded systems. II 74, 359--381 (1980), , J. Math. Anal. Appl.

#### The structural operator $F$ and its role in the theory of retarded systems. I

Delfour, M. C. et Manitius, A., The structural operator $F$ and its role in the theory of retarded systems. I 73, 466--490 (1980), , J. Math. Anal. Appl.

#### The largest class of hereditary systems defining a $C_{0}$ semigroup on the product space

Delfour, M. C., The largest class of hereditary systems defining a $C_{0}$ semigroup on the product space 32, 969--978 (1980), , Canad. J. Math.

#### $F$-reduction of the operator Riccati equation for hereditary differential systems

Delfour, M. C., Lee, E. B. et Manitius, A., $F$-reduction of the operator Riccati equation for hereditary differential systems 14, 385--395 (1978), , Automatica---J. IFAC

#### State theory of linear hereditary differential systems

Delfour, M. C., State theory of linear hereditary differential systems 60, 8--35 (1977), , J. Math. Anal. Appl.

#### Compte rendu du Deuxième Colloque CRM-IRIA

M. C. Delfour, Compte rendu du Deuxième Colloque CRM-IRIA 1, no. 2, (1977), , Ann. Sci. Math. Québec

#### The linear quadratic optimal control problem for hereditary differential systems: theory and numerical solution

Delfour, M. C., The linear quadratic optimal control problem for hereditary differential systems: theory and numerical solution 3, 101--162 (1976), , Appl. Math. Optim.

#### Stability and the infinite-time quadratic cost problem for linear hereditary differential systems

Delfour, M. C., McCalla, C. et Mitter, S. K., Stability and the infinite-time quadratic cost problem for linear hereditary differential systems 13, 48--88 (1975), , SIAM J. Control

#### Hereditary differential systems with constant delays. II. A class of affine systems and the adjoint problem

Delfour, M. C. et Mitter, S. K., Hereditary differential systems with constant delays. II. A class of affine systems and the adjoint problem 18, 18--28 (1975), , J. Differential Equations

#### Actes du Colloque sur la théorie des systèmes et la gestion scientifique des services publics

M. C. Delfour et A. Haurie, Actes du Colloque sur la théorie des systèmes et la gestion scientifique des services publics , (1975), , ACFAS - CRM - HEC, Montréal.

#### Individual and collective rationality in a dynamic Pareto equilibrium

Haurie, A. et Delfour, M. C., Individual and collective rationality in a dynamic Pareto equilibrium 13, 290--302 (1974), , J. Optimization Theory Appl.

#### Function spaces with a projective limit structure

Delfour, Michel C., Function spaces with a projective limit structure 42, 554--568 (1973), , J. Math. Anal. Appl.

#### Hereditary differential systems with constant delays. I. General case

Delfour, M. C. et Mitter, S. K., Hereditary differential systems with constant delays. I. General case 12, 213--235; erratum, ibid. 14\ (1973), 397 (1972), , J. Differential Equations

#### Controllability and observability for infinite-dimensional systems

Delfour, M. C. et Mitter, S. K., Controllability and observability for infinite-dimensional systems 10, 329--333 (1972), , SIAM J. Control

#### Controllability, observability and optimal feedback control of affine hereditary differential systems

Delfour, M. C. et Mitter, S. K., Controllability, observability and optimal feedback control of affine hereditary differential systems 10, 298--328 (1972), , SIAM J. Control

#### Le contrôle optimal de systèmes gouvernés par des équations différentielles héréditaires affines

Delfour, Michel et Mitter, Sanjoy, Le contrôle optimal de systèmes gouvernés par des équations différentielles héréditaires affines 272, A1715--A1718 (1971), , C. R. Acad. Sci. Paris Sér. A-B

#### Systèmes d'équations différentielles héréditaires à retards fixes. Une classe de systèmes affines et le problème du système adjoint

Delfour, Michel et Mitter, Sanjoy, Systèmes d'équations différentielles héréditaires à retards fixes. Une classe de systèmes affines et le problème du système adjoint 272, A1109--A1112 (1971), , C. R. Acad. Sci. Paris Sér. A-B

#### Systémes d'équations différentielles héréditaires à retards fixes. Théorèmes d'existence et d'unicité

Delfour, Michel et Mitter, Sanjoy, Systémes d'équations différentielles héréditaires à retards fixes. Théorèmes d'existence et d'unicité 272, A382--A385 (1971), , C. R. Acad. Sci. Paris Sér. A-B

#### Reachability of perturbed systems and ${\rm min\,sup}$ problems

Delfour, M. C. et Mitter, S. K., Reachability of perturbed systems and ${\rm min\,sup}$ problems 7, 521--533 (1969), , SIAM J. Control

### Awards and Recognition

• Société royale du Canada Les Académies des arts, des lettres et des sciences du Canada, 1997
• Association francophone pour le savoir (Acfas) Prix Urgel-Archambault, 1995
• Conseil des arts du Canada Bourse Killam, 1989