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Author : Halijah Osman
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.:/5 (175 download)
Download or read book Stability Theory for Autonomous Systems written by Halijah Osman and published by . This book was released on 1987 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : N.P. Bhatia
Publisher : Springer Science & Business Media
ISBN 13 : 9783540427483
Total Pages : 252 pages
Book Rating : 4.4/5 (274 download)
Download or read book Stability Theory of Dynamical Systems written by N.P. Bhatia and published by Springer Science & Business Media. This book was released on 2002-01-10 with total page 252 pages. Available in PDF, EPUB and Kindle. 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."
Author : Francesco Amato
Publisher : John Wiley & Sons
ISBN 13 : 1119140528
Total Pages : 184 pages
Book Rating : 4.1/5 (191 download)
Download or read book Finite-Time Stability: An Input-Output Approach written by Francesco Amato and published by John Wiley & Sons. This book was released on 2018-10-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.
Author : William Pallister Richardson
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (643 download)
Download or read book Stability Theory for Plane Autonomous Systems written by William Pallister Richardson and published by . This book was released on 1968 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Urabe
Publisher : Academic Press
ISBN 13 : 008095541X
Total Pages : 343 pages
Book Rating : 4.0/5 (89 download)
Download or read book Nonlinear Autonomous Oscillations: Analytical Theory written by Urabe and published by Academic Press. This book was released on 1967-01-01 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Autonomous Oscillations presents a self-contained and readable account for mathematicians, physicists, and engineers. This monograph is mainly concerned with the analytical theory of nonlinear autonomous oscillations, with the approach based mostly on the author's work. After some introductory material, in Chapter 5 a moving orthogonal coordinate system along a closed orbit is introduced. In the next four chapters, stability theory and perturbation theory are systematically discussed for general autonomous systems by means of a moving coordinate system. In Chapter 10, the two-dimensional autonomous system is discussed in detail on the basis of results obtained in the preceding chapters. In Chapter 11, a numerical method for determining a periodic solution of the general nonlinear autonomous system is described. To illustrate this, the periodic solutions of the autonomous van der Pol equation for various values of thedamping coefficient are computed. Chapter 12, which is based on the work of the author and Sibuya, discusses the center of higher dimension. Chapter 13 discusses a particular inverse problem connected with the period of periodicsolutions of one interesting equation. There are, of course, many other topics of importance in the theory of nonlinear autonomous oscillations. These are, however, omitted in the present monograph because they are mainly topological rather than analytical and in order to keep the book from growing inordinately long.
Author : Luis Barreira
Publisher : Springer
ISBN 13 : 3540747753
Total Pages : 288 pages
Book Rating : 4.5/5 (47 download)
Download or read book Stability of Nonautonomous Differential Equations written by Luis Barreira and published by Springer. This book was released on 2007-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Author : Jacques Leopold Willems
Publisher :
ISBN 13 :
Total Pages : 228 pages
Book Rating : 4.F/5 ( download)
Download or read book Stability Theory of Dynamical Systems written by Jacques Leopold Willems and published by . This book was released on 1970 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : José Mildred Castro
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.E/5 ( download)
Download or read book Stability in Autonomous Systems written by José Mildred Castro and published by . This book was released on 1970 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ratnadip Adhikari
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659342196
Total Pages : 84 pages
Book Rating : 4.3/5 (421 download)
Download or read book A Treatise on Stability of Autonomous and Non-autonomous Systems written by Ratnadip Adhikari and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a stable dynamical system, we broadly mean the one whose overall behavior does not substantially change when its initial conditions or inputs undergo small disturbances. Stability is the fundamental requirement of any practically useful system. The behavior of an unstable system cannot be controlled and hence such a system is simply useless for practical purpose. The aim of this book is to present a concise study of the stability theories of autonomous (time-invariant) and non-autonomous (time-varying) systems. Various related notions and terminologies are meticulously explained. A major focus of the book is on the celebrated Liapunov's direct method which is so far the best mathematical technique for determining the stability nature of a dynamical system. The book introduces and lucidly discusses about the theory of stability of non-autonomous systems which is a complicated subject, having various pitfalls and peculiarities. All concepts in the book are accompanied with illustrative mathematical examples, selected from standard books and journals.
Author : David R. Merkin
Publisher : Springer Science & Business Media
ISBN 13 : 1461240468
Total Pages : 334 pages
Book Rating : 4.4/5 (612 download)
Download or read book Introduction to the Theory of Stability written by David R. Merkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many books on stability theory of motion have been published in various lan guages, including English. Most of these are comprehensive monographs, with each one devoted to a separate complicated issue of the theory. Generally, the examples included in such books are very interesting from the point of view of mathematics, without necessarily having much practical value. Usually, they are written using complicated mathematical language, so that except in rare cases, their content becomes incomprehensible to engineers, researchers, students, and sometimes even to professors at technical universities. The present book deals only with those issues of stability of motion that most often are encountered in the solution of scientific and technical problems. This allows the author to explain the theory in a simple but rigorous manner without going into minute details that would be of interest only to specialists. Also, using appropriate examples, he demonstrates the process of investigating the stability of motion from the formulation of a problem and obtaining the differential equations of perturbed motion to complete analysis and recommendations. About one fourth of the examples are from various areas of science and technology. Moreover, some of the examples and the problems have an independent value in that they could be applicable to the design of various mechanisms and devices. The present translation is based on the third Russian edition of 1987.
Author : David N. Cheban
Publisher : Nova Publishers
ISBN 13 : 9781626189416
Total Pages : 287 pages
Book Rating : 4.1/5 (894 download)
Download or read book Lyapunov Stability of Non-Autonomous Dynamical Systems written by David N. Cheban and published by Nova Publishers. This book was released on 2013 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817644865
Total Pages : 516 pages
Book Rating : 4.8/5 (176 download)
Download or read book Stability of Dynamical Systems written by and published by Springer Science & Business Media. This book was released on 2008 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Zhendong Sun
Publisher : Springer Science & Business Media
ISBN 13 : 0857292560
Total Pages : 266 pages
Book Rating : 4.8/5 (572 download)
Download or read book Stability Theory of Switched Dynamical Systems written by Zhendong Sun and published by Springer Science & Business Media. This book was released on 2011-01-06 with total page 266 pages. Available in PDF, EPUB and Kindle. 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.
Author : David A. Sanchez
Publisher : Courier Dover Publications
ISBN 13 : 0486837599
Total Pages : 179 pages
Book Rating : 4.4/5 (868 download)
Download or read book Ordinary Differential Equations and Stability Theory: written by David A. Sanchez and published by Courier Dover Publications. This book was released on 2019-09-18 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.
Author : J. P. LaSalle
Publisher : SIAM
ISBN 13 : 0898710227
Total Pages : 81 pages
Book Rating : 4.8/5 (987 download)
Download or read book The Stability of Dynamical Systems written by J. P. LaSalle and published by SIAM. This book was released on 1976-01-01 with total page 81 pages. Available in PDF, EPUB and Kindle. 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.
Author : Xiaoxin Liao
Publisher : Elsevier
ISBN 13 : 0080550614
Total Pages : 719 pages
Book Rating : 4.0/5 (85 download)
Download or read book Stability of Dynamical Systems written by Xiaoxin Liao and published by Elsevier. This book was released on 2007-08-01 with total page 719 pages. Available in PDF, EPUB and Kindle. 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
Author : David R. Merkin
Publisher : Springer
ISBN 13 : 9781461240471
Total Pages : 320 pages
Book Rating : 4.2/5 (44 download)
Download or read book Introduction to the Theory of Stability written by David R. Merkin and published by Springer. This book was released on 2011-09-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many books on stability theory of motion have been published in various lan guages, including English. Most of these are comprehensive monographs, with each one devoted to a separate complicated issue of the theory. Generally, the examples included in such books are very interesting from the point of view of mathematics, without necessarily having much practical value. Usually, they are written using complicated mathematical language, so that except in rare cases, their content becomes incomprehensible to engineers, researchers, students, and sometimes even to professors at technical universities. The present book deals only with those issues of stability of motion that most often are encountered in the solution of scientific and technical problems. This allows the author to explain the theory in a simple but rigorous manner without going into minute details that would be of interest only to specialists. Also, using appropriate examples, he demonstrates the process of investigating the stability of motion from the formulation of a problem and obtaining the differential equations of perturbed motion to complete analysis and recommendations. About one fourth of the examples are from various areas of science and technology. Moreover, some of the examples and the problems have an independent value in that they could be applicable to the design of various mechanisms and devices. The present translation is based on the third Russian edition of 1987.
