Author : Clark Robinson
Publisher : CRC Press
Page : 522 pages
File Size : 19,76 MB
Release : 1998-11-17
Category : Mathematics
ISBN : 1482227878
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 : N.P. Bhatia
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 13,63 MB
Release : 2002-01-10
Category : Science
ISBN : 9783540427483
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 : Ju H. Park
Publisher : Springer
Page : 240 pages
File Size : 40,38 MB
Release : 2018-08-09
Category : Technology & Engineering
ISBN : 3319962027
This book introduces the principle theories and applications of control and filtering problems to address emerging hot topics in feedback systems. With the development of IT technology at the core of the 4th industrial revolution, dynamic systems are becoming more sophisticated, networked, and advanced to achieve even better performance. However, this evolutionary advance in dynamic systems also leads to unavoidable constraints. In particular, such elements in control systems involve uncertainties, communication/transmission delays, external noise, sensor faults and failures, data packet dropouts, sampling and quantization errors, and switching phenomena, which have serious effects on the system’s stability and performance. This book discusses how to deal with such constraints to guarantee the system’s design objectives, focusing on real-world dynamical systems such as Markovian jump systems, networked control systems, neural networks, and complex networks, which have recently excited considerable attention. It also provides a number of practical examples to show the applicability of the presented methods and techniques. This book is of interest to graduate students, researchers and professors, as well as R&D engineers involved in control theory and applications looking to analyze dynamical systems with constraints and to synthesize various types of corresponding controllers and filters for optimal performance of feedback systems.
Author : Xiaoxin Liao
Publisher : Elsevier
Page : 719 pages
File Size : 24,92 MB
Release : 2007-08-01
Category : Mathematics
ISBN : 0080550614
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 : Ju H. Park
Publisher : Springer Nature
Page : 351 pages
File Size : 47,34 MB
Release : 2019-08-29
Category : Science
ISBN : 9811392544
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 : James D. Meiss
Publisher : SIAM
Page : 410 pages
File Size : 50,87 MB
Release : 2017-01-24
Category : Mathematics
ISBN : 161197464X
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
Author : Azar, Ahmad Taher
Publisher : IGI Global
Page : 706 pages
File Size : 14,7 MB
Release : 2018-02-09
Category : Computers
ISBN : 1522540784
Complex systems are pervasive in many areas of science. With the increasing requirement for high levels of system performance, complex systems has become an important area of research due to its role in many industries. Advances in System Dynamics and Control provides emerging research on the applications in the field of control and analysis for complex systems, with a special emphasis on how to solve various control design and observer design problems, nonlinear systems, interconnected systems, and singular systems. Featuring coverage on a broad range of topics, such as adaptive control, artificial neural network, and synchronization, this book is an important resource for engineers, professionals, and researchers interested in applying new computational and mathematical tools for solving the complicated problems of mathematical modeling, simulation, and control.
Author : Ju H. Park
Publisher : Springer Nature
Page : 548 pages
File Size : 25,90 MB
Release : 2020-08-11
Category : Technology & Engineering
ISBN : 3030491234
This edited book introduces readers to new analytical techniques and controller design schemes used to solve the emerging “hottest” problems in dynamic control systems and networks. In recent years, the study of dynamic systems and networks has faced major changes and challenges with the rapid advancement of IT technology, accompanied by the 4th Industrial Revolution. Many new factors that now have to be considered, and which haven’t been addressed from control engineering perspectives to date, are naturally emerging as the systems become more complex and networked. The general scope of this book includes the modeling of the system itself and uncertainty elements, examining stability under various criteria, and controller design techniques to achieve specific control objectives in various dynamic systems and networks. In terms of traditional stability matters, this includes the following special issues: finite-time stability and stabilization, consensus/synchronization, fault-tolerant control, event-triggered control, and sampled-data control for classical linear/nonlinear systems, interconnected systems, fractional-order systems, switched systems, neural networks, and complex networks. In terms of introducing graduate students and professional researchers studying control engineering and applied mathematics to the latest research trends in the areas mentioned above, this book offers an excellent guide.
Author : Robert Devaney
Publisher : CRC Press
Page : 280 pages
File Size : 36,69 MB
Release : 2018-03-09
Category : Mathematics
ISBN : 0429981937
The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
Author : V. Lakshmikantham
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 24,73 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1475724497
From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain. It is therefore natural to ask whether it is possible to provide a framework which permits us to handle both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. In this monograph, we present the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we introduce dynamic systems on time scales and prove the basic properties of solutions of such dynamic systems. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the monograph are as follows: It is the first book that is dedicated to a systematic development of the theory of dynamic systems on time scales which is of recent origin. It demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework. It provides an impetus to investigate in the setup of time scales other important problems which might offer a better understanding of the intricacies of a unified study.£/LIST£ Audience: The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets.
