Jamal Daafouz & Sophie Tarbouriech 
Hybrid Systems with Constraints [EPUB ebook] 

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.

İçerik tablosu

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

1.3. Discretization of positive switched systems with sparsity constraints 10

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

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

2.5. Switched discrete-time Lur’e system controlled by the switching law 46

2.6. Conclusion 51

2.7. Bibliography 52

Chapter 3. Stability of Switched DAEs 57
Stephan TRENN

3.1. Introduction 57

3.2. Preliminaries 62

3.3. Stability results 71

3.4. Conclusion 81

3.5. Acknowledgments 81

3.6. Bibliography 81

Chapter 4. Stabilization of Persistently Excited Linear Systems 85
Yacine CHITOUR, Guilherme MAZANTI and Mario SIGALOTTI

4.1. Introduction 86

4.2. Finite-dimensional systems 89

4.3. Infinite-dimensional systems 101

4.4. Further discussion and open problems 110

4.5. Bibliography 118

Chapter 5. Hybrid Coordination of Flow Networks 121
Claudio De PERSIS, Paolo FRASCA

5.1. Introduction 121

5.2. Flow network model and problem statement 123

5.3. Self-triggered gossiping control of flow networks 125

5.4. Practical load balancing 127

5.5. Load balancing with delayed actuation and skewed clocks 132

5.6. Asymptotical load balancing 136

5.7. Conclusions 141

5.8. Acknowledgments 141

5.9. Bibliography 141

Chapter 6. Control of Hybrid Systems: An Overview of Recent Advances 145
Ricardo G. SANFELICE

6.1. Introduction 145

6.2. Preliminaries 149

6.3. Stabilization of hybrid systems 151

6.4. Static state feedback stabilizers 155

6.5. Passivity-based control 159

6.6. Tracking control 169

6.7. Conclusions 176

6.8. Acknowledgments 176

6.9. Bibliography 177

Chapter 7. Exponential Stability for Hybrid Systems with Saturations 179
Mirko FIACCHINI, Sophie TARBOURIECH, Christophe PRIEUR

7.1. Introduction 179

7.2. Problem statement 181

7.3. Set theory and invariance for nonlinear systems: brief overview 185

7.4. Quadratic stability for saturated hybrid systems 190

7.5. Computational issues 203

7.6. Numerical examples 205

7.7. Conclusions 207

7.8. Bibliography 208

Chapter 8. Reference Mirroring for Control with Impacts 213
Fulvio FORNI, Andrew R. TEEL, Luca ZACCARIAN

8.1. Introduction 213

8.2. Hammering a surface 216

8.3. Global tracking of a Newton’s cradle 224

8.4. Global tracking in planar triangles 230

8.5. Global state estimation on n-dimensional convex polyhedra 240

8.6. Proof of the main theorems 247

8.7. Conclusions 251

8.8. Acknowledgments 252

8.9. Bibliography 252

List of Authors 257

Index 261

Yazar hakkında

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.