Qualitative Theory of Hybrid Dynamical Systems

Qualitative Theory of Hybrid Dynamical Systems by Alexey S. Matveev, Andrey V. Savkin.

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 essenti...

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Bibliographic Details
Main Authors: Matveev, Alexey S. (Author), Savkin, Andrey V. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2000.
Edition:1st ed. 2000.
Series:Control Engineering,
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
System theory.
Control engineering.
Robotics.
Mechatronics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Introduction
  • 1.1 Hybrid Dynamical Systems
  • 1.2 Two Contrasting Examples of Discretely Controlled Continuous Variable Systems
  • 1.3 The Main Goal of This Book
  • 1.4 Organization of the Book
  • 1.5 List of Notations
  • 2 Qualitative Analysis of Some Simple Hybrid Dynamical Systems
  • 2.1 Introduction
  • 2.2 Differential Automata and Their Trajectories
  • 2.3 Cyclic Linear Differential Automata
  • 2.4 Qualitative Analysis of Cyclic Linear Differential Automata
  • 2.5 Switched Server Systems with a Cyclic Switching Policy
  • 2.6 Switched Server Systems with Several Limit Cycles
  • 2.7 Qualitative Analysis of Closed Switched Server Systems
  • 2.8 Essentially Non-Periodic Dynamics of Switched Arrival Systems
  • 3 General Theory of Multivalued Differential Automata
  • 3.1 Introduction
  • 3.2 Multivalued Differential Automata
  • 3.3 Decomposition of Well-Posed Differential Automata
  • 3.4 Existence of Periodic Trajectories
  • 3.5 Proofs of the Theorems and Lemmas from Section 3.2
  • 3.6 Proof of Theorem 3.2.26
  • 3.7 Proofs of the Theorems from Sections 3.3 and 3.4
  • 4 Two-Dimensional Hybrid Dynamical Systems
  • 4.1 Introduction
  • 4.2 An Analog of the Poincaré-Bendixon Theorem
  • 4.3 A Switched Arrival System with Three Buffers
  • 4.4 A Switched Server System with Three Buffers
  • 4.5 Proofs of the Statements from Section 4.2
  • 5 Limit Cycles in Hybrid Dynamical Systems with Constant Derivatives: General Theory
  • 5.1 Introduction
  • 5.2 Basic Assumptions and Definitions
  • 5.3 Criteria for Existence and Stability of Limit Cycles
  • 5.4 Proofs of the Lemmas from Section 5.2
  • 5.5 Proofs of the Theorems and Lemmas from Section 5.3.
  • 5.6 Proofs of the Theorem and Lemmas from Subsection 5.3.1
  • 6 Limit Cycles in Hybrid Dynamical Systems with Constant Derivatives: Examples
  • 6.1 Introduction
  • 6.2 Qualitative Analysis of a Switched Server System
  • 6.3 A Switched Arrival System with Three Buffers
  • 6.4 Qualitative Analysis of Switched Single Server Flow Networks
  • 7 Globally Periodic Behavior of Switched Single Server Flow Networks
  • 7.1 Introduction
  • 7.2 Description of Switched Single Server Flow Networks
  • 7.3 Analysis of Switched Single Server Flow Networks
  • 8 Regularizability of Switched Multiple Server Flow Networks
  • 8.1 Introduction 315 8.2 Description of Switched Multiple Server Flow Networks
  • 8.3 Regularizable Switched Multiple Server Flow Networks
  • 8.4 Illustrative Example
  • 9 Open Problems
  • 9.1 Introduction
  • 9.2 Switched Server Systems
  • 9.3 Essentially Nonperiodic Multidimensional Switched Arrival Systems
  • 9.4 Switched Server/Arrival Systems with Several Servers
  • 9.5 A Generalized Processor Sharing Model
  • 9.6 Stabilizability of Switched Multiple Server Flow Networks
  • 9.7 Chaotic Switched Flow Networks
  • 9.8 Existence and Global Stability of Limit Cycles in Nonlinear Differential Automata
  • References.

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