Nonlinear Systems
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Author | : P. G. Drazin |
Publisher | : Cambridge University Press |
Total Pages | : 354 |
Release | : 1992-06-26 |
Genre | : Mathematics |
ISBN | : 9780521406680 |
The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.
Author | : Shankar Sastry |
Publisher | : Springer Science & Business Media |
Total Pages | : 690 |
Release | : 2013-04-18 |
Genre | : Mathematics |
ISBN | : 1475731086 |
There has been much excitement over the emergence of new mathematical techniques for the analysis and control of nonlinear systems. In addition, great technological advances have bolstered the impact of analytic advances and produced many new problems and applications which are nonlinear in an essential way. This book lays out in a concise mathematical framework the tools and methods of analysis which underlie this diversity of applications.
Author | : M. Vidyasagar |
Publisher | : SIAM |
Total Pages | : 515 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9780898719185 |
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 | : Jean Levine |
Publisher | : Springer Science & Business Media |
Total Pages | : 322 |
Release | : 2009-05-28 |
Genre | : Technology & Engineering |
ISBN | : 3642008399 |
This book examines control of nonlinear systems. Coverage ranges from mathematical system theory to practical industrial control applications. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation.
Author | : Jack K. Hale |
Publisher | : Courier Dover Publications |
Total Pages | : 193 |
Release | : 2015-03-24 |
Genre | : Mathematics |
ISBN | : 0486803260 |
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction provides a unified approach for obtaining periodic solutions to nonautonomous and autonomous differential equations. 1963 edition.
Author | : Ivo Petráš |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2011-05-30 |
Genre | : Technology & Engineering |
ISBN | : 3642181015 |
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.
Author | : Juan I. Yuz |
Publisher | : Springer Science & Business Media |
Total Pages | : 288 |
Release | : 2013-10-17 |
Genre | : Technology & Engineering |
ISBN | : 1447155629 |
Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: · the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; · although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and · the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either partially or completely erroneous. They also deal with linear and nonlinear, deterministic and stochastic cases. The impact of the ideas presented on several standard problems in signals and systems is illustrated using a number of applications. Academic researchers and graduate students in systems, control and signal processing will find the ideas presented in Sampled-data Models for Linear and Nonlinear Systems to be a useful manual for dealing with sampled-data systems, clearing away mistaken ideas and bringing the subject thoroughly up to date. Researchers in statistics and economics will also derive benefit from the reworking of ideas relating a model derived from data sampling to an original continuous system.
Author | : Horacio Márquez |
Publisher | : Wiley-Interscience |
Total Pages | : 376 |
Release | : 2003-04-25 |
Genre | : Science |
ISBN | : 9780471427995 |
Provides complete coverage of both the Lyapunov and Input-Output stability theories, ina readable, concise manner. * Supplies an introduction to the popular backstepping approach to nonlinear control design * Gives a thorough discussion of the concept of input-to-state stability * Includes a discussion of the fundamentals of feedback linearization and related results. * Details complete coverage of the fundamentals of dissipative system's theory and its application in the so-called L2gain control prooblem, for the first time in an introductory level textbook. * Contains a thorough discussion of nonlinear observers, a very important problem, not commonly encountered in textbooksat this level. *An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
Author | : Iasson Karafyllis |
Publisher | : Springer Science & Business Media |
Total Pages | : 401 |
Release | : 2011-04-02 |
Genre | : Technology & Engineering |
ISBN | : 0857295136 |
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 | : Wassim M. Haddad |
Publisher | : Princeton University Press |
Total Pages | : 975 |
Release | : 2011-09-19 |
Genre | : Mathematics |
ISBN | : 1400841046 |
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.