April 14, 2021

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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 : 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.

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 Theory of Dynamical Systems

Stability Theory of Dynamical Systems
Author : Jacques Leopold Willems
Publisher : Wiley-Interscience
Release Date : 1970
Category : Dynamical systems
Total pages :201
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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.

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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Dynamical Systems

Dynamical Systems
Author : Clark Robinson,Clark (Northwestern University Robinson, Evanston Illinois USA)
Publisher : AMACOM Div American Mgmt Assn
Release Date : 1999
Category : Mathematics
Total pages :506
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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; 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.

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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Stability Regions of Nonlinear Dynamical Systems

Stability Regions of Nonlinear Dynamical Systems
Author : Hsiao-Dong Chiang,Luís F. C. Alberto
Publisher : Cambridge University Press
Release Date : 2015-07-31
Category : Mathematics
Total pages :450
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An authoritative treatment by leading researchers covering theory and optimal estimation, along with practical applications.

Hybrid Dynamical Systems

Hybrid Dynamical Systems
Author : Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel
Publisher : Princeton University Press
Release Date : 2012-03-18
Category : Mathematics
Total pages :232
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Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Nonlinear Dynamical Systems and Control

Nonlinear Dynamical Systems and Control
Author : Wassim M. Haddad,VijaySekhar Chellaboina
Publisher : Princeton University Press
Release Date : 2011-09-19
Category : Mathematics
Total pages :944
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Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

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 : 2003-06-24
Category : Language Arts & Disciplines
Total pages :430
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The twenty-one invited chapters in this book are an outgrowth of a workshop to honor Anthony N. Michel on the occasion of his retirement. The workshop provided a venue for researchers, colleagues, friends, and students to pay tribute to Michel's significant contributions to the systems and control community; at the same time, the workshop also served as a forum to explore topics and applications related to the stability and control of dynamical systems. His work is characterized both by great depth, as exemplified by his contributions to stability theory of dynamical systems, and by great breadth, as demonstrated by the wide range of problems he has addressed. The chapters are thematically organized into three main areas related to Michel's work. Part 1 contains seven chapters examining issues in stability analysis of dynamical systems; Part 2 includes six chapters dealing with artificial neural networks and signal processing; Part 3 contains eight chapters treating power systems and control systems.

Stability Theory of Dynamical Systems

Stability Theory of Dynamical Systems
Author : N.P. Bhatia,G.P. Szegö
Publisher : Springer Science & Business Media
Release Date : 2002-01-10
Category : Science
Total pages :225
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Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."

Lectures on Dynamical Systems, Structural Stability, and Their Applications

Lectures on Dynamical Systems, Structural Stability, and Their Applications
Author : Kotik K. Lee
Publisher : World Scientific
Release Date : 1992
Category : Science
Total pages :454
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The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.

Stability Theory of Switched Dynamical Systems

Stability Theory of Switched Dynamical Systems
Author : Zhendong Sun,Shuzhi Sam Ge
Publisher : Springer Science & Business Media
Release Date : 2011-01-06
Category : Technology & Engineering
Total pages :256
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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.