The Stability of Dynamical Systems

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

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

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

Stability of Dynamical Systems

Stability of Dynamical Systems
Author: R. K. Brayton,C. H. Tong
Publsiher: Anonim
Total Pages: 23
Release: 1978
ISBN 10:
ISBN 13: OCLC:476029146
Language: EN, FR, DE, ES & NL

Stability of Dynamical Systems Book Review:

Dynamical Systems

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

Dynamical Systems Stability Theory and Applications

Dynamical Systems  Stability Theory and Applications
Author: Nam P. Bhatia,George P. Szegö
Publsiher: Springer
Total Pages: 416
Release: 2006-11-14
ISBN 10: 354034974X
ISBN 13: 9783540349747
Language: EN, FR, DE, ES & NL

Dynamical Systems Stability Theory and Applications Book Review:

Global Stability of Dynamical Systems

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.

Stability Theory of Switched Dynamical Systems

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 Theory of Dynamical Systems

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

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

Uncertain Dynamical Systems

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 Regions of Nonlinear Dynamical Systems

Stability Regions of Nonlinear Dynamical Systems
Author: Hsiao-Dong Chiang,Luís F. C. Alberto
Publsiher: Cambridge University Press
Total Pages: 450
Release: 2015-07-31
ISBN 10: 1107035406
ISBN 13: 9781107035409
Language: EN, FR, DE, ES & NL

Stability Regions of Nonlinear Dynamical Systems Book Review:

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
Publsiher: Princeton University Press
Total Pages: 944
Release: 2011-09-19
ISBN 10: 1400841046
ISBN 13: 9781400841042
Language: EN, FR, DE, ES & NL

Nonlinear Dynamical Systems and Control Book Review:

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.

Lectures on Dynamical Systems Structural Stability and Their Applications

Lectures on Dynamical Systems  Structural Stability  and Their Applications
Author: Kotik K. Lee
Publsiher: World Scientific
Total Pages: 454
Release: 1992
ISBN 10: 9789971509651
ISBN 13: 9971509652
Language: EN, FR, DE, ES & NL

Lectures on Dynamical Systems Structural Stability and Their Applications Book Review:

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.

Differentiable Dynamical Systems

Differentiable Dynamical Systems
Author: Lan Wen
Publsiher: American Mathematical Soc.
Total Pages: 192
Release: 2016-07-20
ISBN 10: 1470427990
ISBN 13: 9781470427993
Language: EN, FR, DE, ES & NL

Differentiable Dynamical Systems Book Review:

This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.

Dynamical Systems

Dynamical Systems
Author: Clark Robinson,Clark (Northwestern University Robinson, Evanston Illinois USA)
Publsiher: AMACOM Div American Mgmt Assn
Total Pages: 506
Release: 1999
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.

Stability Theory of Dynamical Systems

Stability Theory of Dynamical Systems
Author: Jacques Leopold Willems
Publsiher: Wiley-Interscience
Total Pages: 201
Release: 1970
ISBN 10:
ISBN 13: UOM:39015009819247
Language: EN, FR, DE, ES & NL

Stability Theory of Dynamical Systems Book Review:

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.

Bifurcation and Stability in Nonlinear Dynamical Systems

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.

Stability and Control of Large Scale Dynamical Systems

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.