Linear Time Varying Systems
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Linear Time Varying Systems
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Author : Henri Bourlès
language : en
Publisher: Springer
Release Date : 2011-04-21
Linear Time Varying Systems written by Henri Bourlès and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-21 with Technology & Engineering categories.
The aim of this book is to propose a new approach to analysis and control of linear time-varying systems. These systems are defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as they are actually. The system equations, derived, e.g., from the laws of physics, are gathered to form an intrinsic mathematical object, namely a finitely presented module over a ring of operators. This is strongly connected with the engineering point of view, according to which a system is not a specific set of equations but an object of the material world which can be described by equivalent sets of equations. This viewpoint makes it possible to formulate and solve efficiently several key problems of the theory of control in the case of linear time-varying systems. The solutions are based on algebraic analysis. This book, written for engineers, is also useful for mathematicians since it shows how algebraic analysis can be applied to solve engineering problems. Henri Bourlès is a Professor and holds the industrial automation chair at the Conservatoire national des arts et métiers in France. He has been teaching automation for over 20 years in engineering and graduate schools. Bogdan Marinescu is currently research engineer at the French Transmission System Operator (RTE) and Associate Professor at SATIE-Ecole Normale Supérieure de Cachan.
Linear Time Varying Systems And Sampled Data Systems
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Author : Akira Ichikawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-02-26
Linear Time Varying Systems And Sampled Data Systems written by Akira Ichikawa 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 2001-02-26 with Language Arts & Disciplines categories.
This monograph considers linear optimal regulators, differential games and develops the theory for time-varying systems and jump systems.
Linear Time Varying Systems
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Author : Kostas S. Tsakalis
language : en
Publisher:
Release Date : 1993
Linear Time Varying Systems written by Kostas S. Tsakalis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
Time Varying Systems And Computations
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Author : Patrick DeWilde
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-06-30
Time Varying Systems And Computations written by Patrick DeWilde 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 1998-06-30 with Science categories.
Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari able s or z and it is analytic in a large part of the complex plane. Many important prop erties of the system for which it is a transfer function are related to its analytic prop erties. On the other hand, engineers often encounter small and large matrices which describe (linear) maps between physically important quantities. In both cases similar mathematical and computational problems occur: operators, be they transfer functions or matrices, have to be simplified, approximated, decomposed and realized. Each field has developed theory and techniques to solve the main common problems encountered. Yet, there is a large, mysterious gap between complex function theory and numerical linear algebra. For example, complex function theory has solved the problem to find analytic functions of minimal complexity and minimal supremum norm that approxi e. g. , as optimal mate given values at strategic points in the complex plane. They serve approximants for a desired behavior of a system to be designed. No similar approxi mation theory for matrices existed until recently, except for the case where the matrix is (very) close to singular.
Analysis Of Periodically Time Varying Systems
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Author : John A. Richards
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of Periodically Time Varying Systems written by John A. Richards 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 2012-12-06 with Technology & Engineering categories.
Many of the practical techniques developed for treating systems described by periodic differential equations have arisen in different fields of application; con sequently some procedures have not always been known to workers in areas that might benefit substantially from them. Furthermore, recent analytical methods are computationally based so that it now seems an opportune time for an applications-oriented book to be made available that, in a sense, bridges the fields in which equations with periodic coefficients arise and which draws together analytical methods that are implemented readily. This book seeks to ftll that role, from a user's and not a theoretician's view. The complexities of periodic systems often demand a computational approach. Matrix treatments therefore are emphasized here although algebraic methods have been included where they are useful in their own right or where they establish properties that can be exploited by the matrix approach. The matrix development given calls upon the nomenclature and treatment of H. D'Angelo, Linear Time Varying Systems: Analysis and Synthesis (Boston: Allyn and Bacon 1970) which deals with time-varying systems in general. It is recommended for its modernity and comprehensive approach to systems analysis by matrix methods. Since the present work is applications-oriented no attempt has been made to be complete theoretically by way of presenting all proofs, existence theorems and so on. These can be found in D'Angelo and classic and well-developed treatises such as McLachlan, N. W. : Theory and application of Mathieu functions.
Linear Time Varying Approximations To Nonlinear Dynamical Systems
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Author : Maria Tomas-Rodriguez
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-04
Linear Time Varying Approximations To Nonlinear Dynamical Systems written by Maria Tomas-Rodriguez 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 2010-02-04 with Mathematics categories.
Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.
Short Time Stability In Linear Time Varying Systems
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Author : Peter Dorato
language : en
Publisher:
Release Date : 1961
Short Time Stability In Linear Time Varying Systems written by Peter Dorato and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Stability categories.
The concept of short-time stability finds application in missile and satellite systems where operating times are often of finite duration. Short-time stability assures, in a finite time interval, that all inputs bounded by a prescribed constant Greek epsilon result in outputs bounded by a second prescribed constant. The study of short-time stability is divided into two categories: undriven systems and driven systems. Undriven systems are represented by a set of differential equations. Sufficient conditions for short-time stability are given in terms of the coefficients. Driven systems are represented by their impulse response. A necessary and sufficient condition for short-time stability in driven systems is given directly in terms of impulse response. Sufficient conditions for short-time stability in feedback systems, in terms of the open loop impulse response are also included. In addition the concept of shorttime C-equivalence, essentially a structural stability concept, is introduced. Necessary and sufficient conditions for two systems to be short-time C-equivalent are presented. (Author).
Analysis And Control Of Linear Time Varying Systems
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Author : Henri Bourles
language : en
Publisher: Iste Press - Elsevier
Release Date : 2020-11
Analysis And Control Of Linear Time Varying Systems written by Henri Bourles and has been published by Iste Press - Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11 with Mathematics categories.
The topic of the book is the study of structural properties of linear time-varying systems (in particular, controllability, observability, and stability) using algebraic analysis, and the control of these systems (including reference tracking and disturbance rejection).
Time Varying Discrete Linear Systems
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Author : Aristide Halanay
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Time Varying Discrete Linear Systems written by Aristide Halanay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control applications. If sampling is performed in order to control periodic processes, almost periodic systems are obtained. This is a strong motivation to investigate the discrete-time systems with time-varying coefficients. This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. All these tools aim to solve the problems of stabilization and attenuation of disturbances in the framework of H2- and H-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results.
Modeling And Identification Of Linear Parameter Varying Systems
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Author : Roland Toth
language : en
Publisher: Springer
Release Date : 2010-07-11
Modeling And Identification Of Linear Parameter Varying Systems written by Roland Toth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-11 with Technology & Engineering categories.
Through the past 20 years, the framework of Linear Parameter-Varying (LPV) systems has become a promising system theoretical approach to handle the control of mildly nonlinear and especially position dependent systems which are common in mechatronic applications and in the process industry. The birth of this system class was initiated by the need of engineers to achieve better performance for nonlinear and time-varying dynamics, c- mon in many industrial applications, than what the classical framework of Linear Time-Invariant (LTI) control can provide. However, it was also a p- mary goal to preserve simplicity and “re-use” the powerful LTI results by extending them to the LPV case. The progress continued according to this philosophy and LPV control has become a well established ?eld with many promising applications. Unfortunately, modeling of LPV systems, especially based on measured data (which is called system identi?cation) has seen a limited development sincethebirthoftheframework. Currentlythisbottleneck oftheLPVfra- work is halting the transfer of the LPV theory into industrial use. Without good models that ful?ll the expectations of the users and without the und- standing how these models correspond to the dynamics of the application, it is di?cult to design high performance LPV control solutions. This book aims to bridge the gap between modeling and control by investigating the fundamental questions of LPV modeling and identi?cation. It explores the missing details of the LPV system theory that have hindered the formu- tion of a well established identi?cation framework.