Qualitative Theory of Hybrid Dynamical Systems

1. Front Matter

   Pages i-x

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2. Introduction

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 1-11

3. Qualitative Analysis of Some Simple Hybrid Dynamical Systems

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 13-42

4. General Theory of Multivalued Differential Automata

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 43-104

5. Two-Dimensional Hybrid Dynamical Systems

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 105-218

6. Limit Cycles in Hybrid Dynamical Systems with Constant Derivatives: General Theory

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 219-268

7. Limit Cycles in Hybrid Dynamical Systems with Constant Derivatives: Examples

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 269-303

8. Globally Periodic Behavior of Switched Single Server Flow Networks

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 305-314

9. Regularizability of Switched Multiple Server Flow Networks

   • Alexey S. Matveev, Andrey V. Savkin

   Pages 315-329

10. Open Problems

    • Alexey S. Matveev, Andrey V. Savkin

    Pages 331-337

11. Back Matter

    Pages 339-348

    PDF

Hybrid dynamical systems, both continuous and discrete dynamics and variables, have attracted considerable interest recently. This emerging area is found at the interface of control theory and computer engineering, focusing on the analogue and digital aspects of systems and devices. They are essential for advances in modern digital- controller technology. "Qualitative Theory of Hybrid Dynamical Systems" provides a thorough development and systematic presentation of the foundations and framework for hybrid dynamical systems. The presentation offers an accessible, but precise, development of the mathematical models, conditions for existence of limit cycles, and criteria of their stability. The book largely concentrates on the case of discretely controlled continuous-time systems and their relevance for modeling aspects of flexible manufacturing systems and dynamically routed queuing networks. Features and topics: *differential automata*development and use of the concept "cyclic linear differential automata" (CLDA)*switched single-server flow networks coverage*application to specific models of manufacturing systems and queuing networks*select collection of open problems for the subject*self-contained presentation of topics, with the necessary background This new book is an excellent resource for the study and analysis of hybrid dynamical systems used in systems and control engineering. Researchers, postgraduates and professionals in control engineering and computer engineering will find the book an up-to-date development of the relevant new concepts and tools.

• Computer
• Control engineering
• automata
• calculus
• computer science
• dynamische Systeme
• hybrid dynamical systems
• modeling
• systems and signals

"This study investigates the qualitative behaviour of hybrid systems…. This evolution is described by the coupling of the dynamics of an ODE and that of an automaton. Once the continuous state reaches a prescribed set S, the state of the automaton switches to another state and another ODE is activated. The main theme is the characterization of periodic behaviour of such systems and, when it is obtained, the study of its stability…. This mongraph is an exploration, and its merit is to convince the reader of the difficulty and richness of the topic under investigation." —Zentralblatt Math

• Department of Mathematics and Mechanics, St. Petersburg University, St. Petersburg, Russia

  Alexey S. Matveev

• Department of Electrical and Electronic Engineering, University of Western Australia, Perth, Australia

  Andrey V. Savkin

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