Hybrid Systems with Constraints

Control theory is the main subject of this title, in particular
analysis and control design for hybrid dynamic systems.

The notion of hybrid systems offers a strong theoretical and
unified framework to cope with the modeling, analysis and control
design of systems where both continuous and discrete dynamics
interact. The theory of hybrid systems has been the subject of
intensive research over the last decade and a large number of
diverse and challenging problems have been investigated.
Nevertheless, many important mathematical problems remain
open.

This book is dedicated mainly to hybrid systems with constraints;
taking constraints into account in a dynamic system description has
always been a critical issue in control. New tools are provided
here for stability analysis and control design for hybrid systems
with operating constraints and performance specifications.

Contents

1. Positive Systems: Discretization with Positivity and
   Constraints, Patrizio Colaneri, Marcello Farina, Stephen Kirkland,
   Riccardo Scattolini and Robert Shorten.

2. Advanced Lyapunov Functions for Lur'e Systems, Carlos A.
   Gonzaga, Marc Jungers and Jamal Daafouz.

3. Stability of Switched DAEs, Stephan Trenn.

4. Stabilization of Persistently Excited Linear Systems, Yacine
   Chitour, Guilherme Mazanti and Mario Sigalotti.

5. Hybrid Coordination of Flow Networks, Claudio De Persis, Paolo
   Frasca.

6. Control of Hybrid Systems: An Overview of Recent Advances,
   Ricardo G. Sanfelice.

7. Exponential Stability for Hybrid Systems with Saturations, Mirko
   Fiacchini, Sophie Tarbouriech, Christophe Prieur.

8. Reference Mirroring for Control with Impacts, Fulvio Forni,
   Andrew R. Teel, Luca Zaccarian.

About the Authors

Jamal Daafouz is an expert in the area of switched and polytopic
systems and has published several major results in leading journals
(IEEE TAC, Automatica, Systems and Control Letters, etc.). He
serves as an Associate Editor for the key journal IEEE TAC and is a
member of the Editorial Board of the IEEE CSS society.

Sophie Tarbouriech is an expert in the area of nonlinear systems
with constraints and has published several major results in leading
journals (IEEE TAC, Automatica, Systems and Control Letters, etc.)
and books. She is a member of the Editorial Board of the IEEE CSS
society and has also served as an Associate Editor for the key
journal IEEE TAC.

Mario Sigalotti is an expert in applied mathematics and switched
systems and has published several results in leading journals (IEEE
TAC, Automatica, Systems and Control Letters, etc.). He heads the
INRIA team GECO and is a member of the IFAC Technical Committee on
Distributed Parameter Systems.

Auteur

Jamal Daafouz is an expert in the area of switched and polytopic systems and has published several major results in leading journals (IEEE TAC, Automatica, Systems and Control Letters, etc.). He serves as an Associate Editor for the key journal IEEE TAC and is a member of the Editorial Board of the IEEE CSS society.

Sophie Tarbouriech is an expert in the area of nonlinear systems with constraints and has published several major results in leading journals (IEEE TAC, Automatica, Systems and Control Letters, etc.) and books. She is a member of the Editorial Board of the IEEE CSS society and has also served as an Associate Editor for the key journal IEEE TAC.

Mario Sigalotti is an expert in applied mathematics and switched systems and has published several results in leading journals (IEEE TAC, Automatica, Systems and Control Letters, etc.). He heads the INRIA team GECO and is a member of the IFAC Technical Committee on Distributed Parameter Systems.

Résumé

Control theory is the main subject of this title, in particular analysis and control design for hybrid dynamic systems.
The notion of hybrid systems offers a strong theoretical and unified framework to cope with the modeling, analysis and control design of systems where both continuous and discrete dynamics interact. The theory of hybrid systems has been the subject of intensive research over the last decade and a large number of diverse and challenging problems have been investigated. Nevertheless, many important mathematical problems remain open.
This book is dedicated mainly to hybrid systems with constraints; taking constraints into account in a dynamic system description has always been a critical issue in control. New tools are provided here for stability analysis and control design for hybrid systems with operating constraints and performance specifications.

Contents

1. Positive Systems: Discretization with Positivity and Constraints, Patrizio Colaneri, Marcello Farina, Stephen Kirkland, Riccardo Scattolini and Robert Shorten.
   
   2. Advanced Lyapunov Functions for Lur'e Systems, Carlos A. Gonzaga, Marc Jungers and Jamal Daafouz.
   3. Stability of Switched DAEs, Stephan Trenn.
   4. Stabilization of Persistently Excited Linear Systems, Yacine Chitour, Guilherme Mazanti and Mario Sigalotti.
   5. Hybrid Coordination of Flow Networks, Claudio De Persis, Paolo Frasca.
   6. Control of Hybrid Systems: An Overview of Recent Advances, Ricardo G. Sanfelice.
   7. Exponential Stability for Hybrid Systems with Saturations, Mirko Fiacchini, Sophie Tarbouriech, Christophe Prieur.
   8. Reference Mirroring for Control with Impacts, Fulvio Forni, Andrew R. Teel, Luca Zaccarian.

About the Authors

Jamal Daafouz is an expert in the area of switched and polytopic systems and has published several major results in leading journals (IEEE TAC, Automatica, Systems and Control Letters, etc.). He serves as an Associate Editor for the key journal IEEE TAC and is a member of the Editorial Board of the IEEE CSS society.
Sophie Tarbouriech is an expert in the area of nonlinear systems with constraints and has published several major results in leading journals (IEEE TAC, Automatica, Systems and Control Letters, etc.) and books. She is a member of the Editorial Board of the IEEE CSS society and has also served as an Associate Editor for the key journal IEEE TAC.
Mario Sigalotti is an expert in applied mathematics and switched systems and has published several results in leading journals (IEEE TAC, Automatica, Systems and Control Letters, etc.). He heads the INRIA team GECO and is a member of the IFAC Technical Committee on Distributed Parameter Systems.

Contenu

Preface xi

Chapter 1. Positive Systems: Discretization with Positivity and Constraints 1
Patrizio COLANERI, Marcello FARINA, Stephen KIRKLAND, Riccardo SCATTOLINI and Robert SHORTEN

1.1. Introduction and statement of the problem 1

1.2. Discretization of switched positive systems via Padé transformations 4

1.2.1. Preservation of copositive Lyapunov functions 4

1.2.2. Non-negativity of the diagonal Padé approximation 7

1.2.3. An alternative approximation to the exponential matrix 9

1.3. Discretization of positive switched systems with sparsity constraints 10

1.3.1. Forward Euler discretization 10

1.3.2. The mixed Euler-ZOH discretization 11

1.3.3. The mixed Euler-ZOH discretization for switched systems 14

1.4. Conclusions 18

1.5. Bibliography 18

Chapter 2. Advanced Lyapunov Functions for Lur'e Systems 21
Carlos A. GONZAGA, Marc JUNGERS and Jamal DAAFOUZ

2.1. Introduction 21

2.2. Motivating example 24

2.3. A new Lyapunov Lur'e-type function for discrete-time Lur'e systems 26

2.3.1. Definition of discrete-time Lur'e systems 26

2.3.2. Introduction of a new discrete-time Lyapunov Lur'e-type function 26

2.3.3. Global stability analysis 29

2.3.4. Local stability analysis 30

2.4. Switched discrete-time Lur'e system with arbitrary switching law 37

2.4.1. Definition of the switched discrete-ti…