# Stability Of Dynamical Systems

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## Stability of Dynamical Systems

Author | : Xiaoxin Liao,L.Q. Wang,P. Yu |

Publsiher | : Elsevier |

Total Pages | : 718 |

Release | : 2007-08-01 |

ISBN | : 9780080550619 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Stability of Dynamical Systems Book Excerpt:**

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

Author | : J. P. LaSalle |

Publsiher | : SIAM |

Total Pages | : 81 |

Release | : 1976-01-01 |

ISBN | : 0898710227 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**The Stability of Dynamical Systems Book Excerpt:**

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 of Dynamical Systems

Author | : Anthony N. Michel,Ling Hou,Derong Liu |

Publsiher | : Springer Science & Business Media |

Total Pages | : 501 |

Release | : 2008 |

ISBN | : 0817644865 |

Category | : Language Arts & Disciplines |

Language | : EN, FR, DE, ES & NL |

**Stability of Dynamical Systems Book Excerpt:**

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

Author | : J. P. LaSalle |

Publsiher | : SIAM |

Total Pages | : 81 |

Release | : 1976-01-01 |

ISBN | : 9781611970432 |

Category | : Difference equations |

Language | : EN, FR, DE, ES & NL |

**The Stability of Dynamical Systems Book Excerpt:**

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 Switched Dynamical Systems

Author | : Zhendong Sun,Shuzhi Sam Ge |

Publsiher | : Springer Science & Business Media |

Total Pages | : 256 |

Release | : 2011-01-06 |

ISBN | : 0857292560 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Stability Theory of Switched Dynamical Systems Book Excerpt:**

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 Theory of Dynamical Systems

Author | : N.P. Bhatia,G.P. Szegö |

Publsiher | : Springer Science & Business Media |

Total Pages | : 225 |

Release | : 2002-01-10 |

ISBN | : 9783540427483 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Stability Theory of Dynamical Systems Book Excerpt:**

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 Theory of Dynamical Systems

Author | : Jacques Leopold Willems |

Publsiher | : Unknown |

Total Pages | : 201 |

Release | : 1970 |

ISBN | : 1928374650XXX |

Category | : Automatic control |

Language | : EN, FR, DE, ES & NL |

**Stability Theory of Dynamical Systems Book Excerpt:**

## Dynamical Systems Stability Theory and Applications

Author | : Nam P. Bhatia,George P. Szegö |

Publsiher | : Springer |

Total Pages | : 416 |

Release | : 2006-11-14 |

ISBN | : 354034974X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Dynamical Systems Stability Theory and Applications Book Excerpt:**

## Stable and Random Motions in Dynamical Systems

Author | : Jurgen Moser |

Publsiher | : Princeton University Press |

Total Pages | : 198 |

Release | : 2001-05-06 |

ISBN | : 9780691089102 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Stable and Random Motions in Dynamical Systems Book Excerpt:**

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.

## The Stability of Dynamical Systems

Author | : Joseph P. LaSalle |

Publsiher | : Unknown |

Total Pages | : 76 |

Release | : 1976 |

ISBN | : 1928374650XXX |

Category | : DYNAMICAL SYSTEMS (MATHEMATICAL ANALYSIS) |

Language | : EN, FR, DE, ES & NL |

**The Stability of Dynamical Systems Book Excerpt:**

## Bifurcation and Stability in Nonlinear Dynamical Systems

Author | : Albert C. J. Luo |

Publsiher | : Springer Nature |

Total Pages | : 411 |

Release | : 2020-01-30 |

ISBN | : 3030229106 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Bifurcation and Stability in Nonlinear Dynamical Systems Book Excerpt:**

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.

## Lectures on Dynamical Systems Structural Stability and Their Applications

Author | : Kotik K Lee |

Publsiher | : World Scientific |

Total Pages | : 472 |

Release | : 1992-05-14 |

ISBN | : 981450727X |

Category | : Differentiable dynamical systems |

Language | : EN, FR, DE, ES & NL |

**Lectures on Dynamical Systems Structural Stability and Their Applications Book Excerpt:**

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. Contents:IntroductionTopics in Topology and Differential GeometryIntroduction to Global Analysis and Infinite Dimensional ManifoldsGeneral Theory of Dynamical SystemsStability Theory and Liapunov's Direct MethodIntroduction to the General Theory of Structural StabilityApplications Readership: Applied mathematicians and engineers. Keywords:Asymptotically Stable;Bifurcation;Dispersive Systems;Global Analysis;Integral Flow;Liapunov Functions;Linearization;Nonlinear Dynamical Systems;Stable Manifolds;Structural StabilityReview:“The author's style is clear, formulations of mathematical results are precise … The book helps the reader to create a good global picture of the theory of dynamical systems. The author has gathered a considerable number of facts about dynamical systems in this book, including almost 1000 references, so that it can also serve as a handbook for mathematicians beginning to work in this area … The book is useful not only for technicians, but also for mathematicians, and we recommend it to anyone working in dynamical systems.”Alois Klíc Mathematical Reviews

## Nonlinear Dynamical Systems and Control

Author | : Wassim M. Haddad,VijaySekhar Chellaboina |

Publsiher | : Princeton University Press |

Total Pages | : 944 |

Release | : 2011-09-19 |

ISBN | : 1400841046 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Dynamical Systems and Control Book Excerpt:**

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

Author | : Derong Liu,Panos J. Antsaklis |

Publsiher | : Springer Science & Business Media |

Total Pages | : 432 |

Release | : 2012-12-06 |

ISBN | : 1461200377 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Stability and Control of Dynamical Systems with Applications Book Excerpt:**

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.

## Projected Dynamical Systems and Variational Inequalities with Applications

Author | : Anna Nagurney,Ding Zhang |

Publsiher | : Springer Science & Business Media |

Total Pages | : 296 |

Release | : 2012-12-06 |

ISBN | : 146152301X |

Category | : Business & Economics |

Language | : EN, FR, DE, ES & NL |

**Projected Dynamical Systems and Variational Inequalities with Applications Book Excerpt:**

Equilibrium is a concept used in operations research and economics to understand the interplay of factors and problems arising from competitive systems in the economic world. The problems in this area are large and complex and have involved a variety of mathematical methodologies. In this monograph, the authors have widened the scope of theoretical work with a new approach, `projected dynamical systems theory', to previous work in variational inequality theory. While most classical work in this area is static, the introduction to the theory of projected dynamical systems will allow many real-life dynamic situations and problems to be handled and modeled. This monograph includes: a new theoretical approach, `projected dynamical system', which allows the researcher to model real-life situations more accurately; new mathematical methods allowing researchers to combine other theoretical approaches with the projected dynamical systems approach; a framework in which research can adequately model natural, financial and human (real life) situations in competitive equilibrium problems; the computational and numerical methods for the implementation of the methods and theory discussed in the book; stability analysis, algorithms and computational procedures are offered for each set of applications.

## Stability of Dynamical Systems

Author | : Anthony N. Michel,Ling Hou,Derong Liu |

Publsiher | : Springer |

Total Pages | : 653 |

Release | : 2015-03-30 |

ISBN | : 3319152750 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Stability of Dynamical Systems Book Excerpt:**

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 and Control of Large Scale Dynamical Systems

Author | : Wassim M. Haddad,Sergey G. Nersesov |

Publsiher | : Princeton University Press |

Total Pages | : 390 |

Release | : 2011-12-04 |

ISBN | : 0691153469 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Stability and Control of Large Scale Dynamical Systems Book Excerpt:**

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.

## Stability of Dynamical Systems

Author | : Anthony N. Michel,Ling Hou,Derong Liu |

Publsiher | : Unknown |

Total Pages | : 520 |

Release | : 2011-03-21 |

ISBN | : 9780817671228 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Stability of Dynamical Systems Book Excerpt:**

## Spaces of Dynamical Systems

Author | : Sergei Yu. Pilyugin |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 256 |

Release | : 2019-08-05 |

ISBN | : 3110657163 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Spaces of Dynamical Systems Book Excerpt:**

## A Dynamical Systems Theory of Thermodynamics

Author | : Wassim M. Haddad |

Publsiher | : Princeton University Press |

Total Pages | : 744 |

Release | : 2019-06-04 |

ISBN | : 0691192596 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**A Dynamical Systems Theory of Thermodynamics Book Excerpt:**

A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.