Mario Sigalotti – författare

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.

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.

Linear switched systems are a fascinating field of research, with many theoretical questions arising from applications which require sophisticated mathematical tools for their resolution. This monograph presents a unified theoretical approach for the analysis of stability of continuous-time linear switched systems, organizing and optimizing results scattered throughout literature. Emphasis is placed on the development of a rigorous and complete mathematical theory.

In addition to fundamental tools such as common Lyapunov functions, converse Lyapunov theorems, and maximal Lyapunov exponents, the concept of Barabanov norm is also discussed.  While this is now well understood from a theoretical point of view, it has not received much attention in more application-focused settings, likely because this fundamental object was developed in the context of arbitrary switches but has no immediate equivalent for classes of switching signals subject to various constraints (dwell time, persistent excitation, etc.). One of the aims of this text is to bridge this gap as far as possible by explaining how the main features of Barabanov norms can be generalized for classes of constrained switchings. Throughout the text, the authors maintain a general point of view, rather than treating classes of switching signals separately, by developing an axiomatic approach and identifying structural properties of these classes that allow crucial aspects of the Barabanov norm to be extended. 

This monograph will be a valuable resource for mathematicians and control engineers interested in continuous-time switched linear systems, as well as a definitive reference for more experienced researchers.