Linear Time-Varying Systems Algebraic-Analytic Approach
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
- PDF / 9,337,319 Bytes
- 653 Pages / 429.442 x 659.895 pts Page_size
- 9 Downloads / 214 Views
Henri Bourlès and Bogdan Marinescu
Linear Time-Varying Systems Algebraic-Analytic Approach
ABC
Series Advisory Board P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis
Authors Henri Bourlès SATIE, CNAM/ENS de Cachan 61 Avenue Du President Wilson 94230 Cachan France E-mail: [email protected] [email protected]
ISBN 978-3-642-19726-0
Bogdan Marinescu RTE EDF Transport 9, rue de la Porte de Buc 78000 Versailles, France E-mail: [email protected] and SATIE-Ecole Normale Supérieure de Cachan 61, avenue du Président Wilson 94230 Cachan, France E-mail: [email protected]
e-ISBN 978-3-642-19727-7
DOI 10.1007/978-3-642-19727-7 Lecture Notes in Control and Information Sciences
ISSN 0170-8643
Library of Congress Control Number: 2011925386 c 2011 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper 987654321 springer.com
`a nos ´epouses Corinne et Isabelle, pour leur aide et pour leur patience qui `a ´et´e mise `a l’´epreuve maintes fois
Preface
The aim of this book is to propose a new approach to analysis and control of linear time-varying (LTV) systems. More generally, systems over a ring of operators are considered. In the approach developed here, a system is defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as it is 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 module is nothing but the system equations when one takes into account the obvious fact that there are various equivalent ways to write these equations (in different orders, and using various variables). 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 allowed us to formulate and solve efficiently several key problems of the theory of control in the c
Data Loading...
