Switching in Systems and Control

"In this book under review systems involving a coupling between continuous dynamics and discrete events are considered. Instead of specific hybrid systems a more general category of systems is investigated from a control-theoretic perspective. Here such systems are called switched systems... The book is closed with a note and reference section and a large list of literature. As the author remarks, the book can be used for an advanced graduate course, or it can serve as an introduction to the main research issues and results on switched systems and switching control for research in various areas of control theory." -Zentralblatt Math "This book is a well-structured and clearly written text addressing pertinent issues on stability and control for switched systems. These are regarded as a collection of individual dynamic systems, which are selected to drive the state according to a switching policy... The book also includes two appendices succinctly covering some basic facts on stability and Lie algebras. Interesting notes and additional references complementing the main text on a chapter-by-chapter basis are also included. The book serves well the purpose stated by the author of supporting research and advanced graduate courses on switched systems and control." -Mathematical Reviews "I can envision two ways in which the book can be used in teaching. First, the book can serve as the primary textbook of a graduate course on switching systems that covers the introductory material in Part 1, most of the stability material in Part 2, and a subset of the control applications in Part 3. Alternatively, this book can support the second half of a course on hybrid systems, which would start with an overview of hybrid systems modeling and reachability analysis (not covered in this book) and then proceed to the topic of switching systems, covering only subsets of Parts 2 and 3. ...In both cases, students are likely to appreciate the clear writing style, concise proofs, and unpretentious notation of the book. ...The book's strength is its unified, coherent coverage of the topics. Liberzon is successful in presenting this material in a form that is pleasant to read and yet mathematically accurate." -IEEE Control Systems Magazine "The book is written in depth, and all the topics are closely related to the basic problems in analysis and control of switched systems. Furthermore, all the main results presented here are contributed originally by the author and his collaborators. These results, along with the author's recent work on nonlinear control, play a pioneering role in the area of switched systems and switching control. Therefore, the reviewer recommends this book to all researchers who are interested in studying switched/hybrid systems and their applications. Control theorists and mathematicians will find that this book is a very comprehensive reference source. ...The author has made great efforts in the arrangement of the book so that the content is easier to follow. There are many insightful examples, figures and illustrations, and the author has provided many other resources related to the book in the main text and the 'Notes and References' section. Another feature is that many exercises are scattered throughout the book. The reviewer has many reasons to recommend this book to graduate students and beginners who want to start research in switched systems and switching control. In addition to the distinguished theoretical developments, the reviewer believes that the book is equally valuable to practicing engineers. Most of the results included in the book are applicable to general systems, and many problems originate from practical settings." -IEEE Transactions on Automatic Control

• 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.