Switching in Systems and Control

This book bridges the gap between classical mathematical control theory and the interdisciplinary field of hybrid systems. Presented are theoretical developments in the field of stability analysis and control synthesis of systems that combine continuous dynamics with switching events. The theory of such switched systems is related to the study of hybrid systems, which has recently attracted considerable attention among control theorists, computer scientists, and practicing engineers. Excellent resource for the classroom or for self-study.

The text adopts a progressive approach, presenting elementary concepts informally and more advanced topics with greater rigor Results are first derived for linear systems and then extended to nonlinear systems Full proofs for most results are provided An extensive bibliography and a section of technical and historical notes complete the work

Texte du rabat

This book examines switched systems from a control-theoretic perspective, focusing on stability analysis and control synthesis of systems that combine continuous dynamics with switching events. The theory of such switched systems is related to the study of hybrid systems, which has recently attracted considerable attention among control theorists, computer scientists, and practicing engineers. Aimed at readers with a background in systems and control, this book bridges the gap between classical mathematical control theory and the interdisciplinary field of hybrid systems.

The book is divided into three main parts:

• Part I introduces the classes of systems studied in the book

• Part II develops stability theory for switched systems; it covers single and multiple Lyapunov function analysis methods, Lie-algebraic stability criteria, stability under limited-rate switching, and switched systems with various types of useful special structures

• Part III is devoted to switching control design; it describes several wide classes of continuous-time control systems for which the logic-based switching paradigm emerges naturally as a control design tool. Switching control algorithms for several specific problems are discussed.

The text adopts a progressive approach, presenting elementary concepts informally and more advanced topics with greater rigor. Results are first derived for linear systems and then extended to nonlinear systems. Full proofs for most results are provided. An extensive bibliography and a section of technical and historical notes complete the work.

Requiring only familiarity with the basic theory of linear systems, the book is suitable as a text for a graduate course on switched systems and switching control. It may also serve as an introduction to this active area of research for control theorists and mathematicians, as well as a useful reference for experts in the field.

Résumé
l\lany systems encountered in practice involve a coupling between contin­ uous dynamics and discrete events. Systems in which these two kinds of dynamics coexist and interact are usually called hybrid. For example, the following phenomena give rise to hybrid behavior: a valve or a power switch opening and closing; a thermostat turning the heat on and off; biological cells growing and dividing; a server switching between buffers in a queueing network; aircraft entering, crossing, and leaving an air traffic control region; dynamics of a car changing abruptly due to wheels locking and unlocking on ice. Hybrid systems constitute a relatively new and very active area of current research. They present interesting theoretical challenges and are important in many real-world problems. Due to its inherently interdisci­ plinary nature, the field has attracted the attention of people with diverse backgrounds, primarily computer scientists, applied mathematicians, and engineers. Researchers with a background and interest in continuous-time systems and control theory are concerned primarily with properties of the contin­ uous dynamics, such as Lyapunov stability. A detailed investigation of the discrete behavior, on the other hand, is usually not a goal in itself. In fact, rather than dealing with specifics of the discrete dynamics, it is often use­ ful to describe and analyze a more general category of systems which is known to contain a particular model of interest.

Contenu
I Introduction.- 1 Basic Concepts.- II Stability of Switched Systems.- 2 Stability under Arbitrary Switching.- 3 Stability under Constrained Switching.- III Switching Control.- 4 Systems Not Stabilizable by Continuous Feedback.- 5 Systems with Sensor or Actuator Constraints.- 6 Systems with Large Modeling Uncertainty.- IV Supplementary Material.- A Stability.- A.1 Stability definitions.- A.3 Lyapunov's direct (second) method.- A.4 LaSalle's invariance principle.- A.5 Lyapunov's indirect (first) method.- A.6 Input-to-state stability.- B Lie Algebras.- B.1 Lie algebras and their representations.- B.3 Nilpotent and solvable Lie algebras.- B.4 Semisimple and compact Lie algebras.- Notes and References.- Notation.