Liapunov Functions And Stability In Control Theory

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Liapunov Functions And Stability In Control Theory

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Author : Andrea Bacciotti
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-24

Liapunov Functions And Stability In Control Theory written by Andrea Bacciotti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-24 with Technology & Engineering categories.

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

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Author : Andrea Bacciotti
language : en
Publisher:
Release Date : 2014-01-15

Liapunov Functions And Stability In Control Theory written by Andrea Bacciotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Stability By Liapunov S Matrix Function Method With Applications

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Author : A.A. Martynyuk
language : en
Publisher: CRC Press
Release Date : 1998-08-03

Stability By Liapunov S Matrix Function Method With Applications written by A.A. Martynyuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-03 with Mathematics categories.

"Provides a systematic study of matrix Liapunov functions, incorporating new techniques for the qualitative analysis of nonlinear systems encountered in a wide variety of real-world situations."

Geometric And Numerical Foundations Of Movements

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Author : Jean-Paul Laumond
language : en
Publisher: Springer
Release Date : 2017-05-02

Geometric And Numerical Foundations Of Movements written by Jean-Paul Laumond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-02 with Technology & Engineering categories.

This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.

General Problem Of The Stability Of Motion

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Author : A M Lyapunov
language : en
Publisher: CRC Press
Release Date : 1992-08-28

General Problem Of The Stability Of Motion written by A M Lyapunov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-28 with Science categories.

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.

In Stability Of Differential Inclusions

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Author : Philipp Braun
language : en
Publisher: Springer Nature
Release Date : 2021-07-12

In Stability Of Differential Inclusions written by Philipp Braun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-12 with Mathematics categories.

Lyapunov methods have been and are still one of the main tools to analyze the stability properties of dynamical systems. In this monograph, Lyapunov results characterizing the stability and stability of the origin of differential inclusions are reviewed. To characterize instability and destabilizability, Lyapunov-like functions, called Chetaev and control Chetaev functions in the monograph, are introduced. Based on their definition and by mirroring existing results on stability, analogue results for instability are derived. Moreover, by looking at the dynamics of a differential inclusion in backward time, similarities and differences between stability of the origin in forward time and instability in backward time, and vice versa, are discussed. Similarly, the invariance of the stability and instability properties of the equilibria of differential equations with respect to scaling are summarized. As a final result, ideas combining control Lyapunov and control Chetaev functions to simultaneously guarantee stability, i.e., convergence, and instability, i.e., avoidance, are outlined. The work is addressed at researchers working in control as well as graduate students in control engineering and applied mathematics.

Nasa Scientific And Technical Reports

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Author : United States. National Aeronautics and Space Administration Scientific and Technical Information Division
language : en
Publisher:
Release Date : 1967

Nasa Scientific And Technical Reports written by United States. National Aeronautics and Space Administration Scientific and Technical Information Division and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Aeronautics categories.

Finite Time Stability Tools For Control And Estimation

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Author : Denis Efimov
language : en
Publisher:
Release Date : 2021-12-09

Finite Time Stability Tools For Control And Estimation written by Denis Efimov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-09 with Computers categories.

This monograph presents some existing and new results on analysis and design of finite-time and fixed-time converging systems. Two main groups of approaches for analysis/synthesis of this kind of convergence, Lyapunov functions and the theory of homogeneous systems, are considered.The authors focus on the dynamics described by ordinary differential equations, time-delay models and partial differential equations. Some popular control and estimation algorithms, which possess accelerated converge rates, are also reviewed. Finally, the issues of discretization of finite-/fixed-time converging systems are discussed.Divided into 3 parts, this monograph provides the reader with a complete and accessible review of the topic. In the first part, the definitions of the different finite-/fixed-time stability properties are given together with their characterizations via the Lyapunov function approach. In the second part, several stabilization algorithms for linear and nonlinear systems are formalized, which are based on the implicit Lyapunov function approach. In the third part, the issues of discretization of finite-/fixed-time stable systems are discussed, with a special attention to the solutions obtained with the implicit Lyapunov function method. Finally, the accelerated converge concepts are presented for systems described by time-delay and partial differential equations.This monograph is an excellent introduction to the complex field of Finite-Time Stability Tools. It enables the reader to synthesize the important concepts and further their own research in the area.

Stability And Stabilization Of Nonlinear Systems

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Author : Iasson Karafyllis
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-02

Stability And Stabilization Of Nonlinear Systems written by Iasson Karafyllis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-02 with Technology & Engineering categories.

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.

Nonlinear Systems Stability Analysis

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Author : Seyed Kamaleddin Yadavar Nikravesh
language : en
Publisher: CRC Press
Release Date : 2018-09-03

Nonlinear Systems Stability Analysis written by Seyed Kamaleddin Yadavar Nikravesh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Science categories.

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.