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Dynamical Systems Stability Theory and Applications

Dynamical Systems  Stability Theory and Applications Book
Author : Nam P. Bhatia,George P. Szegö
Publisher : Springer
Release : 2006-11-14
ISBN : 354034974X
Language : En, Es, Fr & De

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Book Description :

Download Dynamical Systems Stability Theory and Applications book written by Nam P. Bhatia,George P. Szegö, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Stability of Dynamical Systems

The Stability of Dynamical Systems Book
Author : J. P. LaSalle
Publisher : SIAM
Release : 1976
ISBN : 9781611970432
Language : En, Es, Fr & De

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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 Theory of Dynamical Systems

Stability Theory of Dynamical Systems Book
Author : N.P. Bhatia,G.P. Szegö
Publisher : Springer Science & Business Media
Release : 2002-01-10
ISBN : 9783540427483
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Anthony N. Michel,Ling Hou,Derong Liu
Publisher : Springer
Release : 2015-03-30
ISBN : 3319152750
Language : En, Es, Fr & De

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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 examples.” - Alessandro Astolfi, IEEE Control Systems Magazine, February 2009

Stability of Dynamical Systems

Stability of Dynamical Systems Book
Author : Xiaoxin Liao,L.Q. Wang,P. Yu
Publisher : Elsevier
Release : 2007-08-01
ISBN : 9780080550619
Language : En, Es, Fr & De

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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

Global Stability of Dynamical Systems

Global Stability of Dynamical Systems Book
Author : Michael Shub,A. Fathi,R. Langevin
Publisher : Springer Science & Business Media
Release : 1987
ISBN : 0987650XXX
Language : En, Es, Fr & De

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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

Stability of Dynamical Systems Book
Author : Anthony N. Michel,Ling Hou,Derong Liu
Publisher : Springer Science & Business Media
Release : 2008
ISBN : 0817644865
Language : En, Es, Fr & De

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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.

The Stability of Dynamical Systems

The Stability of Dynamical Systems Book
Author : Joseph P. LaSalle
Publisher : Unknown
Release : 1976
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Stability of Dynamical Systems book written by Joseph P. LaSalle, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Impulsive and Hybrid Dynamical Systems

Impulsive and Hybrid Dynamical Systems Book
Author : Wassim M. Haddad,VijaySekhar Chellaboina,Sergey G. Nersesov
Publisher : Princeton University Press
Release : 2014-09-08
ISBN : 1400865247
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Jacques Leopold Willems
Publisher : Wiley-Interscience
Release : 1970
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Stability Theory of Dynamical Systems book written by Jacques Leopold Willems, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Uncertain Dynamical Systems

Uncertain Dynamical Systems Book
Author : A.A. Martynyuk,Yu. A. Martynyuk-Chernienko
Publisher : CRC Press
Release : 2011-11-28
ISBN : 1439876878
Language : En, Es, Fr & De

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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

Hybrid Dynamical Systems

Hybrid Dynamical Systems Book
Author : Rafal Goebel,Ricardo G. Sanfelice
Publisher : Princeton University Press
Release : 2012-03-18
ISBN : 0691153892
Language : En, Es, Fr & De

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Book Description :

Filled with a wealth of examples to illustrate concepts, this title 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.

Dynamical Systems

Dynamical Systems Book
Author : R. Clark Robinson
Publisher : CRC-Press
Release : 1998-12-01
ISBN : 9780849384950
Language : En, Es, Fr & De

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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.

Interconnected Dynamical Systems

Interconnected Dynamical Systems Book
Author : André Titli,G. Authie,J. L. Calvet
Publisher : North Holland
Release : 1982
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Interconnected Dynamical Systems book written by André Titli,G. Authie,J. L. Calvet, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Stability Theory of Switched Dynamical Systems

Stability Theory of Switched Dynamical Systems Book
Author : Zhendong Sun,Shuzhi Sam Ge
Publisher : Springer Science & Business Media
Release : 2011-01-06
ISBN : 9780857292568
Language : En, Es, Fr & De

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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.

Nonlinear Dynamical Systems and Control

Nonlinear Dynamical Systems and Control Book
Author : Wassim M. Haddad,VijaySekhar Chellaboina
Publisher : Princeton University Press
Release : 2011-09-19
ISBN : 1400841046
Language : En, Es, Fr & De

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Book Description :

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.

Predictability Stability and Chaos in N Body Dynamical Systems

Predictability  Stability  and Chaos in N Body Dynamical Systems Book
Author : Archie E. Roy
Publisher : Springer
Release : 2012-03-17
ISBN : 9781468459999
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Yuri Kifer
Publisher : Birkhäuser
Release : 2012-05-27
ISBN : 9781461581833
Language : En, Es, Fr & De

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Book Description :

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.

Lyapunov Stability of Non Autonomous Dynamical Systems

Lyapunov Stability of Non Autonomous Dynamical Systems Book
Author : David N. Cheban
Publisher : Nova Science Pub Incorporated
Release : 2013-01-01
ISBN : 9781626189263
Language : En, Es, Fr & De

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Book Description :

The foundation of the modern theory of stability was created in the works of A. Poincare and A.M. Lyapunov. The theory of the stability of motion has gained increasing significance in the last decade as is apparent from the large number of publications on the subject. A considerable part of these works are concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering, which first gave the decisive impetus for the expansion and modern development of stability theory. This book contains a systematic exposition of the elements of the asymptotic stability theory of general non-autonomous dynamical systems in metric spaces with an emphasis on the application for different classes of non-autonomous evolution equations (Ordinary Differential Equations (ODEs), Difference Equations (DEs), Functional-Differential Equations (FDEs), Semi-Linear Parabolic Equations etc). The basic results of this book are contained in the courses of lectures which the author has given during many years for the students of the State University of Moldova. This book is intended for mathematicians (scientists and university professors) who are working in the field of stability theory of differential/difference equations, dynamical systems and control theory. It would also be of use for the graduate and post graduate student who is interested in the theory of dynamical systems and its applications. The reader needs no deep knowledge of special branches of mathematics, although it should be easier for readers who know the fundamentals concepts of the theory of metric spaces, qualitative theory of differential/difference equations and dynamical systems.