Stability Of Dynamical Systems

Author : Anonim
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 50,9 Mb
Release : 2008
Category : Differentiable dynamical systems
ISBN : 9780817644864

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Stability of Dynamical Systems by Anonim Pdf

In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers 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 * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems 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 applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.

Author : N.P. Bhatia,G.P. Szegö
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 50,5 Mb
Release : 2002-01-10
Category : Science
ISBN : 3540427481

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Stability Theory of Dynamical Systems by N.P. Bhatia,G.P. Szegö Pdf

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."

Author : Michael Shub
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 46,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475719475

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Global Stability of Dynamical Systems by Michael Shub Pdf

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.

Author : J. P. LaSalle
Publisher : SIAM
Page : 81 pages
File Size : 46,6 Mb
Release : 1976-01-01
Category : Difference equations
ISBN : 1611970431

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The Stability of Dynamical Systems by J. P. LaSalle Pdf

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.

Author : Xiaoxin Liao,L.Q. Wang,P. Yu
Publisher : Elsevier
Page : 719 pages
File Size : 50,9 Mb
Release : 2007-08-01
Category : Mathematics
ISBN : 9780080550619

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Stability of Dynamical Systems by Xiaoxin Liao,L.Q. Wang,P. Yu Pdf

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

Author : Nam Parshad Bhatia,G. P. Szegö
Publisher : Unknown
Page : 440 pages
File Size : 49,6 Mb
Release : 1967
Category : Science
ISBN : STANFORD:36105031722619

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Dynamical Systems: Stability Theory and Applications by Nam Parshad Bhatia,G. P. Szegö Pdf

Author : Zhendong Sun,Shuzhi Sam Ge
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 53,7 Mb
Release : 2011-01-06
Category : Technology & Engineering
ISBN : 9780857292568

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Stability Theory of Switched Dynamical Systems by Zhendong Sun,Shuzhi Sam Ge Pdf

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.

Author : Lan Wen
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 43,7 Mb
Release : 2016-07-20
Category : Differential equations
ISBN : 9781470427993

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Differentiable Dynamical Systems by Lan Wen Pdf

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.

Author : Clark Robinson
Publisher : CRC Press
Page : 522 pages
File Size : 41,8 Mb
Release : 1998-11-17
Category : Mathematics
ISBN : 9781482227871

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Dynamical Systems by Clark Robinson Pdf

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

Author : Nam P. Bhatia,George P. Szegö
Publisher : Springer
Page : 423 pages
File Size : 48,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540349747

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Dynamical Systems: Stability Theory and Applications by Nam P. Bhatia,George P. Szegö Pdf

Author : Wassim M. Haddad,Sergey G. Nersesov
Publisher : Princeton University Press
Page : 390 pages
File Size : 45,9 Mb
Release : 2011-12-04
Category : Mathematics
ISBN : 9780691153469

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Stability and Control of Large-Scale Dynamical Systems by Wassim M. Haddad,Sergey G. Nersesov Pdf

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.

Author : Jacques Leopold Willems
Publisher : Unknown
Page : 228 pages
File Size : 50,9 Mb
Release : 1970
Category : Science
ISBN : STANFORD:36105032612512

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Stability Theory of Dynamical Systems by Jacques Leopold Willems Pdf

Author : Albert C. J. Luo
Publisher : Springer Nature
Page : 418 pages
File Size : 46,6 Mb
Release : 2020-01-30
Category : Mathematics
ISBN : 9783030229108

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Bifurcation and Stability in Nonlinear Dynamical Systems by Albert C. J. Luo Pdf

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.

Author : Ju H. Park,Tae H. Lee,Yajuan Liu,Jun Chen
Publisher : Springer Nature
Page : 335 pages
File Size : 41,6 Mb
Release : 2019-08-29
Category : Science
ISBN : 9789811392542

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Dynamic Systems with Time Delays: Stability and Control by Ju H. Park,Tae H. Lee,Yajuan Liu,Jun Chen Pdf

This book presents up-to-date research developments and novel methodologies to solve various stability and control problems of dynamic systems with time delays. First, it provides the new introduction of integral and summation inequalities for stability analysis of nominal time-delay systems in continuous and discrete time domain, and presents corresponding stability conditions for the nominal system and an applicable nonlinear system. Next, it investigates several control problems for dynamic systems with delays including H(infinity) control problem Event-triggered control problems; Dynamic output feedback control problems; Reliable sampled-data control problems. Finally, some application topics covering filtering, state estimation, and synchronization are considered. The book will be a valuable resource and guide for graduate students, scientists, and engineers in the system sciences and control communities.

Author : A.A. Martynyuk,Yu. A. Martynyuk-Chernienko
Publisher : CRC Press
Page : 310 pages
File Size : 48,5 Mb
Release : 2011-11-28
Category : Mathematics
ISBN : 9781439876879

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Uncertain Dynamical Systems by A.A. Martynyuk,Yu. A. Martynyuk-Chernienko Pdf

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