December 5, 2020

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The Stability of Dynamical Systems

The Stability of Dynamical Systems
Author : J. P. LaSalle
Publisher : SIAM
Release Date : 1976
Category : Difference equations
Total pages :73
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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

Stability of Dynamical Systems
Author : Xiaoxin Liao,L.Q. Wang,P. Yu
Publisher : Elsevier
Release Date : 2007-08-01
Category : Mathematics
Total pages :718
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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

Stability of Dynamical Systems
Author : Anthony N. Michel,Ling Hou,Derong Liu
Publisher : Unknown
Release Date : 2015
Category :
Total pages :129
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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-monotonicLyapunov 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 bookcan 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 examples." - Alessandro Astolfi, IEEE Control Systems Magazine, February 2009.

Global Stability of Dynamical Systems

Global Stability of Dynamical Systems
Author : Michael Shub
Publisher : Springer Science & Business Media
Release Date : 2013-04-17
Category : Mathematics
Total pages :150
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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

Stability of Dynamical Systems
Author : Anthony N. Michel,Ling Hou,Derong Liu
Publisher : Springer Science & Business Media
Release Date : 2008
Category : Language Arts & Disciplines
Total pages :501
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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.

A Comparison of Criteria for Stability in Dynamical Systems

A Comparison of Criteria for Stability in Dynamical Systems
Author : Leo Steg
Publisher : Unknown
Release Date : 1951
Category : Stability
Total pages :206
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Stability of Dynamical Systems

Stability of Dynamical Systems
Author : R. K. Brayton,C. H. Tong
Publisher : Unknown
Release Date : 1978
Category :
Total pages :23
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Dynamical Systems: Stability Theory and Applications

Dynamical Systems: Stability Theory and Applications
Author : Nam P. Bhatia,George P. Szegö
Publisher : Springer
Release Date : 2006-11-14
Category : Mathematics
Total pages :416
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Stability Criteria for Linear Dynamical Systems

Stability Criteria for Linear Dynamical Systems
Author : Brian Porter
Publisher : Unknown
Release Date : 1967
Category : Linear control systems
Total pages :195
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Dynamical Systems

Dynamical Systems
Author : Anonim
Publisher : CRC Press
Release Date : 1998-11-17
Category : Mathematics
Total pages :520
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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

Stability and Control of Large-Scale Dynamical Systems

Stability and Control of Large-Scale Dynamical Systems
Author : Wassim M. Haddad,Sergey G. Nersesov
Publisher : Princeton University Press
Release Date : 2011-12-04
Category : Mathematics
Total pages :371
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Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of technological, environmental, and social phenomena. This book develops stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems.

Dynamical System Theory in Biology: Stability theory and its applications

Dynamical System Theory in Biology: Stability theory and its applications
Author : Robert Rosen
Publisher : John Wiley & Sons
Release Date : 1970
Category : Biomathematics
Total pages :302
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On the Steady Motion and Stability of Dynamical Systems

On the Steady Motion and Stability of Dynamical Systems
Author : Alfred Barnard Basset
Publisher : Unknown
Release Date : 1892
Category : Dynamics
Total pages :7
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Uncertain Dynamical Systems

Uncertain Dynamical Systems
Author : A.A. Martynyuk,Yu. A. Martynyuk-Chernienko
Publisher : CRC Press
Release Date : 2011-11-28
Category : Mathematics
Total pages :310
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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

Stability and Control of Dynamical Systems with Applications
Author : Derong Liu,Panos J. Antsaklis
Publisher : Springer Science & Business Media
Release Date : 2012-12-06
Category : Technology & Engineering
Total pages :432
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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.