# Stability of Dynamical Systems

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## The Stability of Dynamical Systems

Author | : J. P. LaSalle |

Publsiher | : SIAM |

Total Pages | : 73 |

Release | : 1976 |

ISBN 10 | : 9781611970432 |

ISBN 13 | : 1611970431 |

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

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

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

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

Publsiher | : Elsevier |

Total Pages | : 718 |

Release | : 2007-08-01 |

ISBN 10 | : 9780080550619 |

ISBN 13 | : 0080550614 |

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

**Stability of Dynamical Systems Book Review:**

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

## Dynamical Systems Stability Theory and Applications

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

Publsiher | : Springer Verlag |

Total Pages | : 416 |

Release | : 1967 |

ISBN 10 | : |

ISBN 13 | : UOM:39015014359908 |

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

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

## 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 10 | : 9783540427483 |

ISBN 13 | : 3540427481 |

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

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

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

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

Publsiher | : Springer Science & Business Media |

Total Pages | : 501 |

Release | : 2008 |

ISBN 10 | : 0817644865 |

ISBN 13 | : 9780817644864 |

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

**Stability of Dynamical Systems Book Review:**

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

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

Publsiher | : Springer |

Total Pages | : 653 |

Release | : 2015-03-30 |

ISBN 10 | : 3319152750 |

ISBN 13 | : 9783319152752 |

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

**Stability of Dynamical Systems Book Review:**

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

## Global Stability of Dynamical Systems

Author | : Michael Shub |

Publsiher | : Springer Science & Business Media |

Total Pages | : 150 |

Release | : 2013-04-17 |

ISBN 10 | : 1475719477 |

ISBN 13 | : 9781475719475 |

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

**Global Stability of Dynamical Systems Book Review:**

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

Author | : Anonim |

Publsiher | : CRC Press |

Total Pages | : 520 |

Release | : 1998-11-17 |

ISBN 10 | : 1482227878 |

ISBN 13 | : 9781482227871 |

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

**Dynamical Systems Book Review:**

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

Author | : A.A. Martynyuk,Yu. A. Martynyuk-Chernienko |

Publsiher | : CRC Press |

Total Pages | : 310 |

Release | : 2011-11-28 |

ISBN 10 | : 1439876878 |

ISBN 13 | : 9781439876879 |

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

**Uncertain Dynamical Systems Book Review:**

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 Switched Dynamical Systems

Author | : Zhendong Sun,Shuzhi Sam Ge |

Publsiher | : Springer Science & Business Media |

Total Pages | : 256 |

Release | : 2011-01-06 |

ISBN 10 | : 9780857292568 |

ISBN 13 | : 0857292560 |

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

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

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 and Control of Large Scale Dynamical Systems

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

Publsiher | : Princeton University Press |

Total Pages | : 384 |

Release | : 2011-11-14 |

ISBN 10 | : 1400842662 |

ISBN 13 | : 9781400842667 |

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

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

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.

## Bifurcation and Stability in Nonlinear Dynamical Systems

Author | : Albert C. J. Luo |

Publsiher | : Springer Nature |

Total Pages | : 411 |

Release | : 2020-01-30 |

ISBN 10 | : 3030229106 |

ISBN 13 | : 9783030229108 |

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

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

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.

## The Stability of Dynamical Systems

Author | : Joseph P. LaSalle |

Publsiher | : Unknown |

Total Pages | : 76 |

Release | : 1976 |

ISBN 10 | : |

ISBN 13 | : OCLC:603651048 |

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

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

## Impulsive and Hybrid Dynamical Systems

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

Publsiher | : Princeton University Press |

Total Pages | : 496 |

Release | : 2014-09-08 |

ISBN 10 | : 1400865247 |

ISBN 13 | : 9781400865246 |

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

**Impulsive and Hybrid Dynamical Systems Book Review:**

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.

## Hybrid Dynamical Systems

Author | : Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel |

Publsiher | : Princeton University Press |

Total Pages | : 232 |

Release | : 2012-03-18 |

ISBN 10 | : 1400842638 |

ISBN 13 | : 9781400842636 |

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

**Hybrid Dynamical Systems Book Review:**

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.

## Dynamical Systems

Author | : Werner Krabs |

Publsiher | : Springer Science & Business Media |

Total Pages | : 238 |

Release | : 2010-08-03 |

ISBN 10 | : 9783642137228 |

ISBN 13 | : 3642137229 |

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

**Dynamical Systems Book Review:**

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.

## Global Stability of Dynamical Systems

Author | : Michael Shub,A. Fathi,R. Langevin |

Publsiher | : Springer Science & Business Media |

Total Pages | : 150 |

Release | : 1987 |

ISBN 10 | : |

ISBN 13 | : UOM:39015015616801 |

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

**Global Stability of Dynamical Systems Book Review:**

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

Author | : R. Clark Robinson |

Publsiher | : CRC-Press |

Total Pages | : 520 |

Release | : 1998-12-01 |

ISBN 10 | : 9780849384950 |

ISBN 13 | : 0849384958 |

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

**Dynamical Systems Book Review:**

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.

## A Stability Technique for Evolution Partial Differential Equations

Author | : Victor A. Galaktionov,Juan Luis Vázquez |

Publsiher | : Springer Science & Business Media |

Total Pages | : 377 |

Release | : 2012-12-06 |

ISBN 10 | : 1461220505 |

ISBN 13 | : 9781461220503 |

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

**A Stability Technique for Evolution Partial Differential Equations Book Review:**

* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

## Periodic Solutions of Nonlinear Dynamical Systems

Author | : Eduard Reithmeier |

Publsiher | : Springer |

Total Pages | : 174 |

Release | : 2006-11-14 |

ISBN 10 | : 3540384278 |

ISBN 13 | : 9783540384274 |

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

**Periodic Solutions of Nonlinear Dynamical Systems Book Review:**

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.