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Stability of Dynamical Systems

Stability of Dynamical Systems
  • Author : Xiaoxin Liao,L.Q. Wang,P. Yu
  • Publisher :Unknown
  • Release Date :2007-08-01
  • Total pages :718
  • ISBN : 0080550614
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Summary : 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
  • Author : J. P. LaSalle
  • Publisher :Unknown
  • Release Date :1976
  • Total pages :73
  • ISBN : 1611970431
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Summary : 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 :Unknown
  • Release Date :2008
  • Total pages :501
  • ISBN : 9780817644864
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Summary : 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: Stability Theory and Applications

Dynamical Systems: Stability Theory and Applications
  • Author : Nam P. Bhatia,George P. Szegö
  • Publisher :Unknown
  • Release Date :2006-11-14
  • Total pages :416
  • ISBN : 9783540349747
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Summary :

Global Stability of Dynamical Systems

Global Stability of Dynamical Systems
  • Author : Michael Shub
  • Publisher :Unknown
  • Release Date :2013-04-17
  • Total pages :150
  • ISBN : 9781475719475
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Summary : 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

Dynamical Systems
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :1998-11-17
  • Total pages :520
  • ISBN : 9781482227871
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Summary : 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

Uncertain Dynamical Systems

Uncertain Dynamical Systems
  • Author : A.A. Martynyuk,Yu. A. Martynyuk-Chernienko
  • Publisher :Unknown
  • Release Date :2011-11-28
  • Total pages :310
  • ISBN : 9781439876879
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Summary : 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 Theory of Dynamical Systems

Stability Theory of Dynamical Systems
  • Author : N.P. Bhatia,G.P. Szegö
  • Publisher :Unknown
  • Release Date :2002-01-10
  • Total pages :225
  • ISBN : 3540427481
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Summary : 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."

Dynamical System Theory in Biology: Stability theory and its applications

Dynamical System Theory in Biology: Stability theory and its applications
  • Author : Robert Rosen
  • Publisher :Unknown
  • Release Date :1970
  • Total pages :302
  • ISBN : UCAL:B2507444
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Summary :

Stability of Dynamical Systems

Stability of Dynamical Systems
  • Author : Anthony N. Michel,Ling Hou,Derong Liu
  • Publisher :Unknown
  • Release Date :2015-03-30
  • Total pages :653
  • ISBN : 9783319152752
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Summary : 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

Lyapunov Stability of Non-Autonomous Dynamical Systems

Lyapunov Stability of Non-Autonomous Dynamical Systems
  • Author : David N. Cheban
  • Publisher :Unknown
  • Release Date :2013-01-01
  • Total pages :275
  • ISBN : 1626189269
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Summary : 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.

Stability Regions of Nonlinear Dynamical Systems

Stability Regions of Nonlinear Dynamical Systems
  • Author : Hsiao-Dong Chiang,Luís F. C. Alberto
  • Publisher :Unknown
  • Release Date :2015-07-31
  • Total pages :450
  • ISBN : 9781107035409
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Summary : An authoritative treatment by leading researchers covering theory and optimal estimation, along with practical applications.

Nonlinear Dynamical Systems and Control

Nonlinear Dynamical Systems and Control
  • Author : Wassim M. Haddad,VijaySekhar Chellaboina
  • Publisher :Unknown
  • Release Date :2011-09-19
  • Total pages :944
  • ISBN : 9781400841042
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Summary : 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 Large-Scale Dynamical Systems

Stability and Control of Large-Scale Dynamical Systems
  • Author : Wassim M. Haddad,Sergey G. Nersesov
  • Publisher :Unknown
  • Release Date :2011-11-14
  • Total pages :384
  • ISBN : 9781400842667
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Summary : Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Hybrid Dynamical Systems

Hybrid Dynamical Systems
  • Author : Rafal Goebel,Ricardo G. Sanfelice
  • Publisher :Unknown
  • Release Date :2012-03-18
  • Total pages :212
  • ISBN : 9780691153896
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Summary : 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.

Periodic Solutions of Nonlinear Dynamical Systems

Periodic Solutions of Nonlinear Dynamical Systems
  • Author : Eduard Reithmeier
  • Publisher :Unknown
  • Release Date :2006-11-14
  • Total pages :174
  • ISBN : 9783540384274
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Summary : Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics.

Dynamical Systems and Control

Dynamical Systems and Control
  • Author : Firdaus E. Udwadia,H.I. Weber,George Leitmann
  • Publisher :Unknown
  • Release Date :2004-05-10
  • Total pages :456
  • ISBN : 0203694589
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Summary : The 11th International Workshop on Dynamics and Control brought together scientists and engineers from diverse fields and gave them a venue to develop a greater understanding of this discipline and how it relates to many areas in science, engineering, economics, and biology. The event gave researchers an opportunity to investigate ideas and techniq

Stability Theory of Switched Dynamical Systems

Stability Theory of Switched Dynamical Systems
  • Author : Zhendong Sun,Shuzhi Sam Ge
  • Publisher :Unknown
  • Release Date :2011-01-06
  • Total pages :256
  • ISBN : 0857292560
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Summary : 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.

Dynamical Systems

Dynamical Systems
  • Author : Werner Krabs
  • Publisher :Unknown
  • Release Date :2010-08-03
  • Total pages :238
  • ISBN : 3642137229
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Summary : At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.

Bifurcation and Stability in Nonlinear Dynamical Systems

Bifurcation and Stability in Nonlinear Dynamical Systems
  • Author : Albert C. J. Luo
  • Publisher :Unknown
  • Release Date :2020-01-30
  • Total pages :411
  • ISBN : 9783030229108
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Summary : This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control. Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums; Discusses dynamics of infinite-equilibrium systems; Demonstrates higher-order singularity.

Qualitative Theory of Dynamical Systems

Qualitative Theory of Dynamical Systems
  • Author : Anthony Michel,Anthony Wang,Bo Hu,Zuhair Nashed,Earl Taft
  • Publisher :Unknown
  • Release Date :2001-01-04
  • Total pages :732
  • ISBN : 0203908295
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Summary : "Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions. Applies the general theory to specific classes of equations. Presents new and expanded material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics."