Qualitative Theory of Hybrid Dynamical Systems
Published on 23. March 2000
Book
Hardback
X, 348 pages
978-0-8176-4141-2 (ISBN)
Description
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.
Reviews / Votes
"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
More details
Series
Edition
2000 ed.
Language
English
Place of publication
Boston
United States
Target group
Professional and scholarly
Research
Product notice
sewn/stitched
Cloth over boards
Illustrations
X, 348 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 26 mm
Weight
708 gr
ISBN-13
978-0-8176-4141-2 (9780817641412)
DOI
10.1007/978-1-4612-1364-2
Schweitzer Classification
Other editions
Additional editions
Alexey S. Matveev | Andrey V. Savkin
Qualitative Theory of Hybrid Dynamical Systems
Book
10/2012
Springer-Verlag New York Inc.
€160.49
Shipment within 15-20 days
Previous edition
Alexey S. Matveev | Andrey V. Savkin
Qualitative Theory of Hybrid Dynamical Systems
Book
01/2000
Birkhäuser Verlag GmbH
€73.04
Article exhausted; check different version
Content
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.- 6.2Qualitative 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.