Mathematics-Dynamical Systems

Stability of dynamical systems: continuous, discontinuous, and discrete systems

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Title (user) : Stability of dynamical systems: continuous, discontinuous, and discrete systemsTitle (google) : Stability of Dynamical Systems Continuous, Discontinuous, and Discrete SystemsISBN : 0817644865,9780817644864GoogleBook ID : s4mq1h0elUkCOpenLibrary ID : OL16522133MEdition : 1Series : Systems & control: foundations & applicationsAuthors (user) : Anthony N. Michel, Ling Hou, Derong LiuAuthors (google) : Anthony N. Michel,Ling Hou,Derong LiuPublisher : BirkhäuserLanguage : EnglishPublication Date : 2008File Format : pdfCategories : Language Arts & Disciplines------------------------------------------Description (user) : In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states...
Description

Title (user) : Stability of dynamical systems: continuous, discontinuous, and discrete systems

Title (google) : Stability of Dynamical Systems Continuous, Discontinuous, and Discrete Systems

ISBN : 0817644865,9780817644864

GoogleBook ID : s4mq1h0elUkC

OpenLibrary ID : OL16522133M

Edition : 1

Series : Systems & control: foundations & applications

Authors (user) : Anthony N. Michel, Ling Hou, Derong Liu

Authors (google) : Anthony N. Michel,Ling Hou,Derong Liu

Publisher : Birkhäuser

Language : English

Publication Date : 2008

File Format : pdf

Categories : Language Arts & Disciplines


------------------------------------------

Description (user) :

In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics.

Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model.

The book covers the following four general topics:

* Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems

Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.


------------------------------------------

Description (google) :
Filling a gap in the literature, this volume offers the first comprehensive analysis of all the major types of system models. Throughout the text, there are many examples and applications to important classes of systems in areas such as power and energy, feedback control, artificial neural networks, digital signal processing and control, manufacturing, computer networks, and socio-economics. Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in a huge variety of fields.


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Table of contents :
Preface......Page 10
Contents......Page 6
Introduction......Page 12
Dynamical Systems......Page 28
Fundamental Theory: The Principal Stability and Boundedness Results on Metric Spaces......Page 82
Fundamental Theory:Specialized Stability and Boundedness Results on Metric Spaces......Page 160
Applications to a Class of Discrete-Event Systems......Page 184
Finite-Dimensional Dynamical Systems......Page 195
Finite-Dimensional Dynamical Systems: Specialized Results......Page 265
Applications to Finite-Dimensional Dynamical Systems......Page 347
Infinite-Dimensional Dynamical Systems......Page 404
Index......Page 498

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