Download or read book The Stabilizability of Infinite Dimensional Linear Time invariant Systems written by Claude David Benchimol and published by . This book was released on 1977 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stabilization of Infinite Dimensional Systems written by El Hassan Zerrik and published by Springer Nature. This book was released on 2021-03-29 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Infinite Dimensional Linear Systems Theory written by Ruth F. Curtain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.
Download or read book Stability of Finite and Infinite Dimensional Systems written by Michael I. Gil' and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Download or read book Stability and Stabilization of Infinite Dimensional Systems with Applications written by Zheng-Hua Luo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robots arms and large space structures. Various control methods such as sensor feedback control and dynamic boundary control are applied to stabilize the equations. Many new theorems and methods are included in the book. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. New results on semigroups and their stability are presented, and readers can learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.
Download or read book Input to state Stability and Stabilizability of Infinite dimensional Linear Systems written by Robert Nabiullin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robustness Measures for Linear Time invariant Time delay Systems written by Guangdi Hu and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Time delays which occur between the inputs and outputs of physical systems are often found in industrial systems, and the presence of such time-delay makes the design of feedback controllers for a system more demanding, since time-delay may tend to destabilize a system. This thesis studies robust measures for characterizing such time-delay systems; in particular, it studies stability robustness of and controllability/stabilizability robustness of linear time-delay systems. The first part of the thesis, analyzes the stability robustness of two types of objects: (1) quasipolynomials, and (2) matrices for linear time-invariant time-delay systems of the retarded and neutral type. In the case of (1), we consider quasipolynomials with affine uncertainties. A general solution for this problem is then obtained by using tools from convex analysis. In the case of (2), we consider a system described by a stable state space model, and we define the real stability radius of a stable system as being the distance of the perturbed system matrix to the set of unstable systems. The results obtained extend the real stability radius for linear time-invariant finite dimensional systems to the case of linear time-invariant infinite dimensional systems. The second part of the thesis, deals with controllability/stabilizability robustness of linear time-invariant finite dimensional systems and spectral controllability/stabilizability robustness of linear time-invariant infinite dimensional systems. We define the real controllablity radius and the real stabilizability radius as being the distance from the nominal system matrix to the set of uncontrollable matrices, and the set of unstabilizable matrices, respectively. The method of solutions for these problems is carried out based on matrix perturbation theory. A number of examples and application studies are included in the thesis to illustrate the type of results which may be obtained.
Download or read book The Extreme Extension Restriction Approach in Infinite Dimensional Linear Time Invariant Systems Theory written by Jingbo Wu and published by . This book was released on 2008-01-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear System Theory written by Lotfi Zadeh and published by Courier Dover Publications. This book was released on 2008-07-24 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: The state space approach is widely used in systems ranging from industrial robots to space guidance control. This landmark in the technique's development and applications was written by two pioneers in the field, Lotfi A. Zadeh and Charles A. Desoer, who teach in the Department of Electrical Engineering and Computer Science at the University of California, Berkeley. Starting with a self-contained introduction to system theory, the authors explain basic concepts, presenting each idea within a carefully integrated framework of numerous illustrative examples. Most of the text concerns the application of the state space approach to systems described by differential equations. Problems of stability and controllability receive particular attention, and connections between the state space approach and classical techniques are highlighted. The properties of transfer functions are covered in separate chapters. Extensive appendixes feature complete and self-contained expositions of delta-functions and distributions, the Laplace and Fourier transform theory, the theory of infinite dimensional linear vector spaces, and functions of a matrix.
Download or read book On stability of linear time varying infinite dimensional discrete time systems written by Krzysztof Maciej Przyłuski and published by . This book was released on 1984 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Robust Control of Infinite Dimensional Systems written by Ciprian Foias and published by Springer. This book was released on 1995-12 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception, H( optimization theory has become the control methodology of choice in robust feedback analysis and design. This monograph presents an operator theoretic approach to the H( control for disturbed parameter systems, that is, systems which admit infinite dimensional state spaces.
Download or read book Infinite Dimensional Linear Systems Theory written by Ruth F. Curtain and published by Springer. This book was released on 1978 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of Linear Time invariant Discrete time Systems written by P. C. M. Vieira and published by . This book was released on 1986 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability for discrete linear systems in hilbert spaces written by and published by . This book was released on 1912 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Este trabalho aborda o problema da estabilidade de sistemas lineares, invariantes no tempo, a tempo discreto, com o espaço de estado sendo um espaço de Hilbert complexo e separável de dimensão infinita. São investigadas condições necessárias e/ou suficientes para quatro conceitos diferentes de estabilidade: estabilidade assintótica uniforme e estabilidade assintótica forte, estabilidade assintótica fraca e estabilidade limitada. Identifica-se e analisa-se as conexões entre os problemas de estabilidade e dois problemas em aberto da teoria de operadores em espaços de Hilbert: o problema do subespaço invariante e o problemas da similaridade e contração. Diversos resultados, oriundos de tentativas de solução para os dois problemas acima, ou motivados por aquelas tentativas, são utilizadas para fornecer caracterizações adicionais (principalmente caracterizações espectrais) para os quatro conceitos de estabilidade em questão.
Download or read book On Arbitrarily Stabilizable Linear Time varying Infinite dimensional Discrete time Systems written by K. Maciej Przyłuski and published by . This book was released on 1997 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On stability of linear infinite dimensional discrete time systems written by Petre Preda and published by . This book was released on 1986 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
