Liapunov Functions And Stability In Control Theory

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Liapunov Functions and Stability in Control Theory

Author : Andrea Bacciotti
Publisher : Springer Science & Business Media
ISBN 13 : 9783540213321
Total Pages : 264 pages
Book Rating : 4.2/5 (133 download)

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Book Synopsis Liapunov Functions and Stability in Control Theory by : Andrea Bacciotti

Download or read book Liapunov Functions and Stability in Control Theory written by Andrea Bacciotti and published by Springer Science & Business Media. This book was released on 2005-04-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g., about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.

Liapunov Functions and Stability in Control Theory

Author : Andrea Bacciotti
Publisher :
ISBN 13 : 9781447139744
Total Pages : 224 pages
Book Rating : 4.1/5 (397 download)

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Book Synopsis Liapunov Functions and Stability in Control Theory by : Andrea Bacciotti

Download or read book Liapunov Functions and Stability in Control Theory written by Andrea Bacciotti and published by . This book was released on 2014-01-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems

Author : V. Lakshmikantham
Publisher : Springer Science & Business Media
ISBN 13 : 9401579393
Total Pages : 182 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems by : V. Lakshmikantham

Download or read book Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi, "', si j'avait su comment en revenir, je n'y serais point all".' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . .'; 'One service logic has rendered com puter science . .'; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Robust Nonlinear Control Design

Author : Randy A. Freeman
Publisher : Springer Science & Business Media
ISBN 13 : 0817647597
Total Pages : 268 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Robust Nonlinear Control Design by : Randy A. Freeman

Download or read book Robust Nonlinear Control Design written by Randy A. Freeman and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This softcover book summarizes Lyapunov design techniques for nonlinear systems and raises important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues, and they report their findings in this text. The researcher who wishes to enter the field of robust nonlinear control could use this book as a source of new research topics. For those already active in the field, the book may serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the techniques presented here.

Nonlinear Dynamical Systems and Control

Author : Wassim M. Haddad
Publisher : Princeton University Press
ISBN 13 : 0691133298
Total Pages : 975 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Nonlinear Dynamical Systems and Control by : Wassim M. Haddad

Download or read book Nonlinear Dynamical Systems and Control written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2008-02-17 with total page 975 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics and beyond. This book presents and develops a complete and thorough treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods.

Partial Stability and Control

Author : V.I. Vorotnikov
Publisher : Springer Science & Business Media
ISBN 13 : 1461241502
Total Pages : 442 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Partial Stability and Control by : V.I. Vorotnikov

Download or read book Partial Stability and Control written by V.I. Vorotnikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the conventional research for the general theory of stability, this mono graph deals with problems on stability and stabilization of dynamic systems with respect not to all but just to a given part of the variables characterizing these systems. Such problems are often referred to as the problems of partial stability (stabilization). They naturally arise in applications either from the requirement of proper performance of a system or in assessing system capa bility. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated: • "Lotka-Volterra ecological principle of extinction;" • focusing and acceleration of particles in electromagnetic fields; • "drift" of the gyroscope axis; • stabilization of a spacecraft by specially arranged relative motion of rotors connected to it. Also very effective is the approach to the problem of stability (stabilization) with respect to all the variables based on preliminary analysis of partial sta bility (stabilization). A. M. Lyapunov, the founder of the modern theory of stability, was the first to formulate the problem of partial stability. Later, works by V. V. Rumyan tsev drew the attention of many mathematicians and mechanicians around the world to this problem, which resulted in its being intensively worked out. The method of Lyapunov functions became the key investigative method which turned out to be very effective in analyzing both theoretic and applied problems.

Stability and Performance of Control Systems with Actuator Saturation

Author : Yuanlong Li
Publisher : Birkhäuser
ISBN 13 : 3319642464
Total Pages : 374 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Stability and Performance of Control Systems with Actuator Saturation by : Yuanlong Li

Download or read book Stability and Performance of Control Systems with Actuator Saturation written by Yuanlong Li and published by Birkhäuser. This book was released on 2017-11-28 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph investigates the stability and performance of control systems subject to actuator saturation. It presents new results obtained by both improving the treatment of the saturation function and constructing new Lyapunov functions. In particular, two improved treatments of the saturation function are described that exploit the intricate structural properties of its traditional convex hull representation. The authors apply these treatments to the estimation of the domain of attraction and the finite-gain L2 performance by using the quadratic Lyapunov function and the composite quadratic Lyapunov function. Additionally, an algebraic computation method is given for the exact determination of the maximal contractively invariant ellipsoid, a level set of a quadratic Lyapunov function. The authors conclude with a look at some of the problems that can be solved by the methods developed and described throughout the book. Numerous step-by-step descriptions, examples, and simulations are provided to illustrate the effectiveness of their results. Stability and Performance of Control Systems with Actuator Saturation will be an invaluable reference for graduate students, researchers, and practitioners in control engineering and applied mathematics.

Constructions of Strict Lyapunov Functions

Author : Michael Malisoff
Publisher : Springer Science & Business Media
ISBN 13 : 1848825358
Total Pages : 386 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Constructions of Strict Lyapunov Functions by : Michael Malisoff

Download or read book Constructions of Strict Lyapunov Functions written by Michael Malisoff and published by Springer Science & Business Media. This book was released on 2009-06-13 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed. This book contains a broad repertoire of Lyapunov constructions for nonlinear systems, focusing on methods for transforming non-strict Lyapunov functions into strict ones. Their explicitness and simplicity make them suitable for feedback design, and for quantifying the effects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples.

The Generation of Liapunov Functions in Automatic Control Theory by an Energy Metric Algorithm

Author : Edward Thomas Wall
Publisher :
ISBN 13 :
Total Pages : 252 pages
Book Rating : 4.:/5 (931 download)

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Book Synopsis The Generation of Liapunov Functions in Automatic Control Theory by an Energy Metric Algorithm by : Edward Thomas Wall

Download or read book The Generation of Liapunov Functions in Automatic Control Theory by an Energy Metric Algorithm written by Edward Thomas Wall and published by . This book was released on 1967 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stability of Dynamical Systems

Author : Anthony N. Michel
Publisher :
ISBN 13 : 9783319152769
Total Pages : pages
Book Rating : 4.1/5 (527 download)

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Book Synopsis Stability of Dynamical Systems by : Anthony N. Michel

Download or read book Stability of Dynamical Systems written by Anthony N. Michel and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover 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 involving monotonic and non-monotonic Lyapunov functions - Specialization of this stability theory to finite-dimensional dynamical systems - Specialization of this stability theory to infinite-dimensional dynamical systems Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this bookcan be used as a textbook for graduate courses in stability theory of dynamical systems. It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences. Review of the First Edition: "The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems. [This] is a very interesting book which complements the existing literature. [It] is clearly written, and difficult concepts are illustrated by means of good examples." - Alessandro Astolfi, IEEE Control Systems Magazine, February 2009.

Work Session in Lyapunov's Second Method

Author : Louis F. Kazda
Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Work Session in Lyapunov's Second Method by : Louis F. Kazda

Download or read book Work Session in Lyapunov's Second Method written by Louis F. Kazda and published by . This book was released on 1962 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lyapunov Matrix Equation in System Stability and Control

Author : Zoran Gajic
Publisher : Elsevier
ISBN 13 : 0080535674
Total Pages : 271 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Lyapunov Matrix Equation in System Stability and Control by : Zoran Gajic

Download or read book Lyapunov Matrix Equation in System Stability and Control written by Zoran Gajic and published by Elsevier. This book was released on 1995-08-14 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lyapunov and Riccati equations are two of the fundamental equations of control and system theory, having special relevance for system identification, optimization, boundary value problems, power systems, signal processing, and communications.The Lyapunov Matrix Equation in System Stability and Control covers mathematical developments and applications while providing quick and easy references for solutions to engineering and mathematical problems. Examples of real-world systems are given throughout the text in order to demonstrate the effectiveness of the presented methods and algorithms.The book will appeal to practicing engineers, theoreticians, applied mathematicians, and graduate students who seek a comprehensive view of the main results of the Lyapunov matrix equation.Presents techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systemsOffers summaries and references at the end of each chapterContains examples of the use of the equation to solve real-world problemsProvides quick and easy references for the solutions to engineering and mathematical problems using the Lyapunov equation

Applications of Liapunov Methods in Stability

Author : A. Halanay
Publisher : Springer Science & Business Media
ISBN 13 : 9401116008
Total Pages : 245 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Applications of Liapunov Methods in Stability by : A. Halanay

Download or read book Applications of Liapunov Methods in Stability written by A. Halanay and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 1992 marks the centennial anniversary of publication of the celebrated monograph "The General Problem of Stability of Motion" written by A. M. Liapunov. This anniversary inspires to think about the way theory and applications have developed during this century. The first observation one can make is that the so-called "second method", nowadays known as the "Liapunov function method", has received more attention than the "first method"; let us also mention the study of critical cases, which brought more attention recently in connection with the study of bifurcations and with nonlinear stabilization. One of the reasons of popularity of the Liapunov function approach might be the fact that, in many situations in science and engineering, and not only in mechanics, which was the main source of inspiration for the work of Liapunov, natural Liapunov functions may be proposed, intimately connected with the properties of the processes. It is one of the purposes of this book to advocate this idea. From the mathematical viewpoint, the century after the first appear ance of Liapunov's monograph has been characterized both by general izations and by refinements of Liapunov's ideas. But we feel that the most spectacular progress is the understanding of the wide possibilities open for applications by the use of Stability Theory as constructed by Liapunov a century ago. We have tried to show some of the ideas in this direction by start ing with our personal experience in the study of some models.

The Interrelationship Between Liapunov Functions and the Performance Criteria of Optimal Control Theory

Author : Edward Moshang
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (526 download)

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Book Synopsis The Interrelationship Between Liapunov Functions and the Performance Criteria of Optimal Control Theory by : Edward Moshang

Download or read book The Interrelationship Between Liapunov Functions and the Performance Criteria of Optimal Control Theory written by Edward Moshang and published by . This book was released on 1965 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stability and Control of Linear Systems

Author : Andrea Bacciotti
Publisher : Springer
ISBN 13 : 3030024059
Total Pages : 200 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Stability and Control of Linear Systems by : Andrea Bacciotti

Download or read book Stability and Control of Linear Systems written by Andrea Bacciotti and published by Springer. This book was released on 2018-11-02 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced textbook introduces the main concepts and advances in systems and control theory, and highlights the importance of geometric ideas in the context of possible extensions to the more recent developments in nonlinear systems theory. Although inspired by engineering applications, the content is presented within a strong theoretical framework and with a solid mathematical background, and the reference models are always finite dimensional, time-invariant multivariable linear systems. The book focuses on the time domain approach, but also considers the frequency domain approach, discussing the relationship between the two approaches, especially for single-input-single-output systems. It includes topics not usually addressed in similar books, such as a comparison between the frequency domain and the time domain approaches, bounded input bounded output stability (including a characterization in terms of canonical decomposition), and static output feedback stabilization for which a simple and original criterion in terms of generalized inverse matrices is proposed. The book is an ideal learning resource for graduate students of control theory and automatic control courses in engineering and mathematics, as well as a reference or self-study guide for engineers and applied mathematicians.

Stability of Dynamical Systems

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817644865
Total Pages : 516 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Stability of Dynamical Systems by :

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.

General Problem of the Stability Of Motion

Author : A M Lyapunov
Publisher : CRC Press
ISBN 13 : 9780748400621
Total Pages : 284 pages
Book Rating : 4.4/5 (6 download)

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Book Synopsis General Problem of the Stability Of Motion by : A M Lyapunov

Download or read book General Problem of the Stability Of Motion written by A M Lyapunov and published by CRC Press. This book was released on 1992-08-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes more widely accessible the text of Lyapunov's major memoir of the general problem of the stability of motion. Translated by A. T. Fuller (University of Cambridge), the work is now available for the first time in the English language, and marked the centenary of the Russian publication in the late 1800s. Including a biography of Lyapunov and a comprehensive bibliography of his work, this excellent volume will prove to be of fundamental interest to all those concerned with the concept of the stability of motion, boundaries of stability, and with nonlinear dynamics.