Stabilization Of Infinite Dimensional Systems

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Stabilization Of Infinite Dimensional Systems

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Author : El Hassan Zerrik
language : en
Publisher: Springer Nature
Release Date : 2021-03-29

Stabilization Of Infinite Dimensional Systems written by El Hassan Zerrik and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-29 with Technology & Engineering categories.

This book deals with the stabilization issue of infinite dimensional dynamical systems both at the theoretical and applications levels. Systems theory is a branch of applied mathematics, which is interdisciplinary and develops activities in fundamental research which are at the frontier of mathematics, automation and engineering sciences. It is everywhere, innumerable and daily, and moreover is there something which is not system: it is present in medicine, commerce, economy, psychology, biological sciences, finance, architecture (construction of towers, bridges, etc.), weather forecast, robotics, automobile, aeronautics, localization systems and so on. These are the few fields of application that are useful and even essential to our society. It is a question of studying the behavior of systems and acting on their evolution. Among the most important notions in system theory, which has attracted the most attention, is stability. The existing literature on systems stability is quite important, but disparate, and the purpose of this book is to bring together in one document the essential results on the stability of infinite dimensional dynamical systems. In addition, as such systems evolve in time and space, explorations and research on their stability have been mainly focused on the whole domain in which the system evolved. The authors have strongly felt that, in this sense, important considerations are missing: those which consist in considering that the system of interest may be unstable on the whole domain, but stable in a certain region of the whole domain. This is the case in many applications ranging from engineering sciences to living science. For this reason, the authors have dedicated this book to extension of classical results on stability to the regional case. This book considers a very important issue, which is that it should be accessible to mathematicians and to graduate engineering with a minimal background in functional analysis. Moreover, for the majority of the students, this would be their only acquaintance with infinite dimensional system. Accordingly, it is organized by following increasing difficulty order. The two first chapters deal with stability and stabilization of infinite dimensional linear systems described by partial differential equations. The following chapters concern original and innovative aspects of stability and stabilization of certain classes of systems motivated by real applications, that is to say bilinear and semi-linear systems. The stability of these systems has been considered from a global and regional point of view. A particular aspect concerning the stability of the gradient has also been considered for various classes of systems. This book is aimed at students of doctoral and master’s degrees, engineering students and researchers interested in the stability of infinite dimensional dynamical systems, in various aspects.

Stability And Stabilization Of Infinite Dimensional Systems With Applications

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Author : Zheng-Hua Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-01-22

Stability And Stabilization Of Infinite Dimensional Systems With Applications written by Zheng-Hua Luo 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 1999-01-22 with Computers categories.

The time evol11tion of many physical phenomena in nat11re can be de scribed by partial differential eq11ations. To analyze and control the dynamic behavior of s11ch systems. infinite dimensional system theory was developed and has been refined over the past several decades. In recent years. stim11lated by the applications arising from space exploration. a11tomated manufact11ring, and other areas of technological advancement, major progress has been made in both theory and control technology associated with infinite dimensional systems. For example, new conditions in the time domain and frequency domain have been derived which guarantee that a Co-semigroup is exponen tially stable; new feedback control laws helVe been proposed to exponentially ;;tabilize beam. wave, and thermoelastic equations; and new methods have been developed which allow us to show that the spectrum-determined growth condition holds for a wide class of systems. Therefore, there is a need for a reference book which presents these restllts in an integrated fashion. Complementing the existing books, e. g . . [1]. [41]. and [128]. this book reports some recent achievements in stability and feedback stabilization of infinite dimensional systems. In particular, emphasis will be placed on the second order partial differential equations. such as Euler-Bernoulli beam equations. which arise from control of numerous mechanical systems stich as flexible robot arms and large space structures. We will be focusing on new results. most of which are our own recently obtained research results.

Stabilization Of Infinite Dimensional Systems Via Periodic Output Feedback

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Author : John R. Zavgren
language : en
Publisher:
Release Date : 1983

Stabilization Of Infinite Dimensional Systems Via Periodic Output Feedback written by John R. Zavgren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Differential equations, Linear categories.

Adaptive Stabilization Of Infinite Dimensional Systems

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Author : Hartmut Logemann
language : de
Publisher:
Release Date : 1990

Adaptive Stabilization Of Infinite Dimensional Systems written by Hartmut Logemann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

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.

Stability Of Finite And Infinite Dimensional Systems

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Author : Michael I Gil'
language : en
Publisher:
Release Date : 1998-09-30

Stability Of Finite And Infinite Dimensional Systems written by Michael I Gil' and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-30 with categories.

Some Remarks On Adaptive Stabilization Of Infinite Dimensional Systems

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Author : Hartmut Logemann
language : de
Publisher:
Release Date : 1990

Some Remarks On Adaptive Stabilization Of Infinite Dimensional Systems written by Hartmut Logemann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

Stabilization And Simultaneous Stabilization Of Infinite Dimensional Systems By Periodic Output Feedback

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Author : Tongzeng Yang
language : en
Publisher:
Release Date : 1989

Stabilization And Simultaneous Stabilization Of Infinite Dimensional Systems By Periodic Output Feedback written by Tongzeng Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Feedback control systems categories.

Robust Stabilization Of Infinite Dimensional Systems By Finite Dimensional Controllers

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Author : Ruth F. Curtain
language : en
Publisher:
Release Date : 1985

Robust Stabilization Of Infinite Dimensional Systems By Finite Dimensional Controllers written by Ruth F. Curtain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.

State Estimation And Stabilization Of Nonlinear Systems

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Author : Abdellatif Ben Makhlouf
language : en
Publisher: Springer Nature
Release Date : 2023-11-06

State Estimation And Stabilization Of Nonlinear Systems written by Abdellatif Ben Makhlouf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Technology & Engineering categories.

This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal for the stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).