The Stability of Dynamical Systems Book

The Stability of Dynamical Systems


  • Author : J. P. LaSalle
  • Publisher : SIAM
  • Release Date : 1976
  • Genre: Difference equations
  • Pages : 73
  • ISBN 10 : 1611970431

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The Stability of Dynamical Systems Book Description :

An introduction to aspects of the theory of dynamial systems based on extensions of Liapunov's direct method. The main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations. The latest results on invariance properties for non-autonomous time-varying systems processes are presented for difference and differential equations.

Stability of Dynamical Systems Book

Stability of Dynamical Systems


  • Author : Xiaoxin Liao
  • Publisher : Elsevier
  • Release Date : 2007-08-01
  • Genre: Mathematics
  • Pages : 718
  • ISBN 10 : 0080550614

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Stability of Dynamical Systems Book Description :

The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers

Stability of Dynamical Systems Book

Stability of Dynamical Systems


  • Author : Anthony N. Michel
  • Publisher : Springer
  • Release Date : 2015-03-30
  • Genre: Science
  • Pages : 653
  • ISBN 10 : 9783319152752

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Stability of Dynamical Systems Book Description :

The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonic Lyapunov functions. Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover 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 involving monotonic and non-monotonic Lyapunov functions - Specialization of this stability theory to finite-dimensional dynamical systems - Specialization of this stability theory to infinite-dimensional dynamical systems Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this book can be used as a textbook for graduate courses in stability theory of dynamical systems. It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences. Review of the First Edition: “The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems. [This] is a very interesting book which complements the existing literature. [It] is clearly written, and difficult concepts are illustrated by means of good

Global Stability of Dynamical Systems Book

Global Stability of Dynamical Systems


  • Author : Michael Shub
  • Publisher : Springer
  • Release Date : 2010-12-05
  • Genre: Mathematics
  • Pages : 150
  • ISBN 10 : 1441930795

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Global Stability of Dynamical Systems Book Description :

These notes are the result of a course in dynamical systems given at Orsay during the 1976-77 academic year. I had given a similar course at the Gradu ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's n-Stability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M.

Stability of Dynamical Systems Book

Stability of Dynamical Systems


  • Author : Anthony N. Michel
  • Publisher : Springer Science & Business Media
  • Release Date : 2008
  • Genre: Language Arts & Disciplines
  • Pages : 501
  • ISBN 10 : 9780817644864

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Stability of Dynamical Systems Book Description :

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.

Dynamical Systems Book

Dynamical Systems


  • Author : R. Clark Robinson
  • Publisher : CRC-Press
  • Release Date : 1998-12-01
  • Genre: Mathematics
  • Pages : 520
  • ISBN 10 : 0849384958

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Dynamical Systems Book Description :

Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included; providing a careful review of background materials; introducing ideas through examples and at a level accessible to a beginning graduate student; focusing on multidimensional systems of real variables. The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects. What's New in the Second Edition?: A revised discussion of the saddle node bifurcation; a new section on the horseshoe for a flow with a transverse homoclinic point; material on horseshoes for nontransverse homoclinic points, indicating recent extensions to the understanding of how horseshoes arise; information proving the ergodicity of a hyperbolic toral automorphism; a new chapter on Hamiltonian systems.

Stability Regions of Nonlinear Dynamical Systems Book

Stability Regions of Nonlinear Dynamical Systems


  • Author : Hsiao-Dong Chiang
  • Publisher : Cambridge University Press
  • Release Date : 2015-07-31
  • Genre: Mathematics
  • Pages : 450
  • ISBN 10 : 9781107035409

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Stability Regions of Nonlinear Dynamical Systems Book Description :

An authoritative treatment by leading researchers covering theory and optimal estimation, along with practical applications.

Uncertain Dynamical Systems Book

Uncertain Dynamical Systems


  • Author : A.A. Martynyuk
  • Publisher : CRC Press
  • Release Date : 2011-11-28
  • Genre: Mathematics
  • Pages : 310
  • ISBN 10 : 9781439876879

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Uncertain Dynamical Systems Book Description :

This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations. Each chapter contains new conditions of stability of unperturbed motion of the abo

Stability and Control of Dynamical Systems with Applications Book

Stability and Control of Dynamical Systems with Applications


  • Author : Derong Liu
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Technology & Engineering
  • Pages : 432
  • ISBN 10 : 9781461200376

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Stability and Control of Dynamical Systems with Applications Book Description :

It is with great pleasure that I offer my reflections on Professor Anthony N. Michel's retirement from the University of Notre Dame. I have known Tony since 1984 when he joined the University of Notre Dame's faculty as Chair of the Depart ment of Electrical Engineering. Tony has had a long and outstanding career. As a researcher, he has made im portant contributions in several areas of systems theory and control theory, espe cially stability analysis of large-scale dynamical systems. The numerous awards he received from the professional societies, particularly the Institute of Electrical and Electronics Engineers (IEEE), are a testament to his accomplishments in research. He received the IEEE Control Systems Society's Best Transactions Paper Award (1978), and the IEEE Circuits and Systems Society's Guillemin-Cauer Prize Paper Award (1984) and Myril B. Reed Outstanding Paper Award (1993), among others. In addition, he was a Fulbright Scholar (1992) and received the Alexander von Hum boldt Forschungspreis (Alexander von Humboldt Research Award for Senior U.S. Scientists) from the German government (1997). To date, he has written eight books and published over 150 archival journal papers. Tony is also an effective administrator who inspires high academic standards.

Stability Theory of Switched Dynamical Systems Book

Stability Theory of Switched Dynamical Systems


  • Author : Zhendong Sun
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-01-06
  • Genre: Technology & Engineering
  • Pages : 256
  • ISBN 10 : 0857292560

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Stability Theory of Switched Dynamical Systems Book Description :

There are plenty of challenging and interesting problems open for investigation in the field of switched systems. Stability issues help to generate many complex nonlinear dynamic behaviors within switched systems. The authors present a thorough investigation of stability effects on three broad classes of switching mechanism: arbitrary switching where stability represents robustness to unpredictable and undesirable perturbation, constrained switching, including random (within a known stochastic distribution), dwell-time (with a known minimum duration for each subsystem) and autonomously-generated (with a pre-assigned mechanism) switching; and designed switching in which a measurable and freely-assigned switching mechanism contributes to stability by acting as a control input. For each of these classes this book propounds: detailed stability analysis and/or design, related robustness and performance issues, connections to other control problems and many motivating and illustrative examples.