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Stability of Dynamical Systems

Stability of Dynamical Systems
A Book

by Xiaoxin Liao,L.Q. Wang,P. Yu

  • Publisher : Elsevier
  • Release : 2007-08-01
  • Pages : 718
  • ISBN : 9780080550619
  • Language : En, Es, Fr & De
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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

The Stability of Dynamical Systems

The Stability of Dynamical Systems
A Book

by J. P. LaSalle

  • Publisher : SIAM
  • Release : 1976
  • Pages : 73
  • ISBN : 9781611970432
  • Language : En, Es, Fr & De
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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.

Dynamical Systems: Stability Theory and Applications

Dynamical Systems: Stability Theory and Applications
A Book

by Nam P. Bhatia,George P. Szegö

  • Publisher : Springer
  • Release : 2006-11-14
  • Pages : 416
  • ISBN : 354034974X
  • Language : En, Es, Fr & De
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Stability Theory of Dynamical Systems

Stability Theory of Dynamical Systems
A Book

by N.P. Bhatia,G.P. Szegö

  • Publisher : Springer Science & Business Media
  • Release : 2002-01-10
  • Pages : 225
  • ISBN : 9783540427483
  • Language : En, Es, Fr & De
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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."

Stability of Dynamical Systems

Stability of Dynamical Systems
On the Role of Monotonic and Non-Monotonic Lyapunov Functions

by Anthony N. Michel,Ling Hou,Derong Liu

  • Publisher : Springer
  • Release : 2015-03-30
  • Pages : 653
  • ISBN : 3319152750
  • Language : En, Es, Fr & De
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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-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 examples.” - Alessandro Astolfi, IEEE Control Systems Magazine, February 2009

The Stability of Dynamical Systems

The Stability of Dynamical Systems
A Book

by Joseph P. LaSalle

  • Publisher : Unknown Publisher
  • Release : 1976
  • Pages : 76
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Global Stability of Dynamical Systems

Global Stability of Dynamical Systems
A Book

by Michael Shub,A. Fathi,R. Langevin

  • Publisher : Springer Science & Business Media
  • Release : 1987
  • Pages : 150
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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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 Theory of Switched Dynamical Systems

Stability Theory of Switched Dynamical Systems
A Book

by Zhendong Sun,Shuzhi Sam Ge

  • Publisher : Springer Science & Business Media
  • Release : 2011-01-06
  • Pages : 256
  • ISBN : 0857292560
  • Language : En, Es, Fr & De
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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.

Stability of Dynamical Systems

Stability of Dynamical Systems
Continuous, Discontinuous, and Discrete Systems

by Anthony N. Michel,Ling Hou,Derong Liu

  • Publisher : Springer Science & Business Media
  • Release : 2008
  • Pages : 501
  • ISBN : 0817644865
  • Language : En, Es, Fr & De
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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.

Impulsive and Hybrid Dynamical Systems

Impulsive and Hybrid Dynamical Systems
Stability, Dissipativity, and Control

by Wassim M. Haddad,VijaySekhar Chellaboina,Sergey G. Nersesov

  • Publisher : Princeton University Press
  • Release : 2014-09-08
  • Pages : 496
  • ISBN : 1400865247
  • Language : En, Es, Fr & De
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This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems. Impulsive and Hybrid Dynamical Systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.

Stability Theory of Dynamical Systems

Stability Theory of Dynamical Systems
A Book

by Jacques Leopold Willems

  • Publisher : Unknown Publisher
  • Release : 1970
  • Pages : 201
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Interconnected Dynamical Systems

Interconnected Dynamical Systems
Stability, Decomposition, and Decentralisation

by André Titli,G. Authie,J. L. Calvet

  • Publisher : North Holland
  • Release : 1982
  • Pages : 330
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Stability of Dynamical Systems

Stability of Dynamical Systems
A Book

by Anthony N. Michel,Ling Hou,Derong Liu

  • Publisher : Unknown Publisher
  • Release : 2011-03-21
  • Pages : 520
  • ISBN : 9780817671228
  • Language : En, Es, Fr & De
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Predictability, Stability, and Chaos in N-Body Dynamical Systems

Predictability, Stability, and Chaos in N-Body Dynamical Systems
A Book

by Archie E. Roy

  • Publisher : Springer
  • Release : 2012-03-17
  • Pages : 616
  • ISBN : 9781468459999
  • Language : En, Es, Fr & De
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The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.

Random Perturbations of Dynamical Systems

Random Perturbations of Dynamical Systems
A Book

by Yuri Kifer

  • Publisher : Birkhäuser
  • Release : 2012-05-27
  • Pages : 294
  • ISBN : 9781461581833
  • Language : En, Es, Fr & De
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Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative theory of ordinary differential equations commonly known nowdays as the theory of dynamical systems. Since physical processes are usually affected by an enormous number of small external fluctuations whose resulting action would be natural to consider as random, the stability of dynamical systems with respect to random perturbations comes into the picture. There are differences between the study of stability properties of single trajectories, i. e. , the Lyapunov stability, and the global stability of dynamical systems. The stochastic Lyapunov stability was dealt with in Hasminskii [Has]. In this book we are concerned mainly with questions of global stability in the presence of noise which can be described as recovering parameters of dynamical systems from the study of their random perturbations. The parameters which is possible to obtain in this way can be considered as stable under random perturbations, and so having physical sense. -1- Our set up is the following.

Stable and Random Motions in Dynamical Systems

Stable and Random Motions in Dynamical Systems
With Special Emphasis on Celestial Mechanics (AM-77)

by Jurgen Moser

  • Publisher : Princeton University Press
  • Release : 2016-03-02
  • Pages : 216
  • ISBN : 1400882699
  • Language : En, Es, Fr & De
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For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

Dynamical Systems

Dynamical Systems
Stability, Symbolic Dynamics, and Chaos

by Anonim

  • Publisher : CRC Press
  • Release : 1998-11-17
  • Pages : 520
  • ISBN : 1482227878
  • Language : En, Es, Fr & De
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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

The Stability of Dynamical Systems

The Stability of Dynamical Systems
A Book

by J. P. LaSalle

  • Publisher : SIAM
  • Release : 1976-01-01
  • Pages : 76
  • ISBN : 0898710227
  • Language : En, Es, Fr & De
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An introduction to aspects of the theory of dynamical 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.

Stability and Control of Large-Scale Dynamical Systems

Stability and Control of Large-Scale Dynamical Systems
A Vector Dissipative Systems Approach

by Wassim M. Haddad,Sergey G. Nersesov

  • Publisher : Princeton University Press
  • Release : 2011-12-04
  • Pages : 371
  • ISBN : 0691153469
  • Language : En, Es, Fr & De
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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.

The Stability of Dynamical Systems

The Stability of Dynamical Systems
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1976
  • Pages : 76
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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