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Author : K. C. Cowan
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (428 download)
Download or read book Stability Analysis of Nonlinear Autonomous Systems by Numerical Methods written by K. C. Cowan and published by . This book was released on 1967 with total page 200 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 : Seyed Kamaleddin Yadavar Nikravesh
Publisher : CRC Press
ISBN 13 : 1466569298
Total Pages : 319 pages
Book Rating : 4.4/5 (665 download)
Download or read book Nonlinear Systems Stability Analysis written by Seyed Kamaleddin Yadavar Nikravesh and published by CRC Press. This book was released on 2018-09-03 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions—system stability being the most crucial property. Without stability, a system will not have value. Nonlinear Systems Stability Analysis: Lyapunov-Based Approach introduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems. Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.
Author : Vangipuram Lakshmikantham
Publisher : Birkhäuser
ISBN 13 : 3319272004
Total Pages : 339 pages
Book Rating : 4.3/5 (192 download)
Download or read book Stability Analysis of Nonlinear Systems written by Vangipuram Lakshmikantham and published by Birkhäuser. This book was released on 2015-12-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Author : M. Vidyasagar
Publisher : SIAM
ISBN 13 : 9780898719185
Total Pages : 515 pages
Book Rating : 4.7/5 (191 download)
Download or read book Nonlinear Systems Analysis written by M. Vidyasagar and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.
Author : Daniel James Stonier
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.:/5 (813 download)
Download or read book Stability Theory and Numerical Analysis of Non-autonomous Dynamical Systems written by Daniel James Stonier and published by . This book was released on 2002 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, concepts emerging from cocycle theory have been redefined to form a comprehensive framework for the study of stability and numerical methods within time-dependent dynamical systems. This new mathematical theory provides a better understanding of the nature of forward and pullback behaviour that is inherent within such systems.
Author : J. P. LaSalle
Publisher : SIAM
ISBN 13 : 9781611970432
Total Pages : 81 pages
Book Rating : 4.9/5 (74 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 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 : Iasson Karafyllis
Publisher : Springer Science & Business Media
ISBN 13 : 0857295136
Total Pages : 401 pages
Book Rating : 4.8/5 (572 download)
Download or read book Stability and Stabilization of Nonlinear Systems written by Iasson Karafyllis and published by Springer Science & Business Media. This book was released on 2011-04-02 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.
Author : Andrew Stuart
Publisher : Cambridge University Press
ISBN 13 : 9780521645638
Total Pages : 708 pages
Book Rating : 4.6/5 (456 download)
Download or read book Dynamical Systems and Numerical Analysis written by Andrew Stuart and published by Cambridge University Press. This book was released on 1998-11-28 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Author : Ali H. Nayfeh
Publisher : John Wiley & Sons
ISBN 13 : 3527617558
Total Pages : 700 pages
Book Rating : 4.5/5 (276 download)
Download or read book Applied Nonlinear Dynamics written by Ali H. Nayfeh and published by John Wiley & Sons. This book was released on 2008-11-20 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
Author : Hsiao-Dong Chiang
Publisher : Cambridge University Press
ISBN 13 : 1316368327
Total Pages : 483 pages
Book Rating : 4.3/5 (163 download)
Download or read book Stability Regions of Nonlinear Dynamical Systems written by Hsiao-Dong Chiang and published by Cambridge University Press. This book was released on 2015-08-13 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation problems.
Author : Luigi Grippo
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (955 download)
Download or read book A New Approach to the Stability Analysis of Non-linear Discrete-time Autonomous Systems written by Luigi Grippo and published by . This book was released on 1973 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.N. Kounadis
Publisher : Springer
ISBN 13 : 3709143462
Total Pages : 418 pages
Book Rating : 4.7/5 (91 download)
Download or read book Nonlinear Stability of Structures written by A.N. Kounadis and published by Springer. This book was released on 2014-05-04 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume gives a very modern treatment of all theoretical as well as computational aspects of nonlinear structural stability. The theoretical part starts with the basic concepts of nonlinear static stability and classical dynamics and proceeds subsequently with recent progress in nonlinear dynamic stability and dynamic buckling of structures including an introduction to chaos. The first paper overviews theory and modelling of various structural instability problems. In the second section, nonlinear dynamic buckling and stability of autonomous discrete dissipative structural systems, gradient and non-gradient are discussed. The third paper handles stability and bifurcation phenomena in dynamical systems. The fourth paper contains an introduction to nonlinear dynamics and chaos. Special attention is devoted to the direct computation of critical points and path-switching strategies. A variety of numerical simulations for complicated nonlinear unstable responses also illustrate this part.
Author : Alexey Victorovich Pavlov
Publisher : Springer Science & Business Media
ISBN 13 : 0817644652
Total Pages : 176 pages
Book Rating : 4.8/5 (176 download)
Download or read book Uniform Output Regulation of Nonlinear Systems written by Alexey Victorovich Pavlov and published by Springer Science & Business Media. This book was released on 2006-07-27 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study of the nonlinear output regulation problem embraces local as well as global cases, covering such aspects as controller design and practical implementation issues. From the reviews: "The authors treat the problem of output regulation for a nonlinear control system...[they] develop a global approach to output regulation along familiar lines....I found the book to be ambitious and rigorous, tackling some hard conceptual issues." --IEEE TRANSACTIONS ON AUTOMATIC CONTROL
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 : 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 : Shuli Guo
Publisher : Springer
ISBN 13 : 9811089086
Total Pages : 268 pages
Book Rating : 4.8/5 (11 download)
Download or read book Stability and Control of Nonlinear Time-varying Systems written by Shuli Guo and published by Springer. This book was released on 2018-04-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents special systems derived from industrial models, including the complex saturation nonlinear functions and the delay nonlinear functions. It also presents typical methods, such as the classical Liapunov and Integral Inequalities methods. Providing constructive qualitative and stability conditions for linear systems with saturated inputs in both global and local contexts, it offers practitioners more concise model systems for modern saturation nonlinear techniques, which have the potential for future applications. This book is a valuable guide for researchers and graduate students in the fields of mathematics, control, and engineering.
