Stability of Forced Discrete-Time Systems
Chapter 3 dealed with dynamic discrete-time systems called free or unforced, because there was no input. A system with input is called a forced system.
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Günter Ludyk
Stability of Time-Variant Discrete-Time Systems
Advances in Control Systems and Signal Processing Editor: lrmfried Hartmann Valurne 5 Volume 1 : Erhard Bühler and Dieter Franke Tropics in ldentification and Distributed Parameter Systems Volume 2: Hubert Hahn Higher Order Root-Locus Technique with Applications in Control System design Bernhard Herz A Gontribution about Centrollability Volume 3: Günter Ludyk Time-Variant Discrete-Time Systems Volume 4: Dietmar Möller/ Dobrivoje Popoviel Georg Thiele Modeling, Simulation and Parameter-Estimstion of the Human Csrdiovascular System Volume 5: Günter Ludyk Stability of Time-Variant Discrete-Time Systems
Günter Ludyk
Stability of Time-Variant Discrete-Time Systems With 20 Figures
Springer Fachmedien Wiesbaden GmbH
CIP-Kurztitelaufnahme der Deutschen Bibliothek Ludyk, Günther: Stability of time-variant discrete-time systems I Günter Ludyk. (Advances in control systems and signal processing; Vol. 51 ISBN 978-3-528-08911-5 ISBN 978-3-663-13932-4 (eBook) DOI 10.1007/978-3-663-13932-4
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Editor: Dr .-1 ng. I. Hartmann Prof. für Regelungstechnik und Systemdynamik Technische Universität Berlin HardenbergstraBe 29c 1000 Berlin 12, West Gerrnany
Author: Dr. lng. G. Ludyk o. Prof. für Regelungstheorie Universität Bremen Postfach 330440 2800 Bremen, West Germany
All rights reserved © Springer Fachmedien Wiesbaden 1985 Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig in 1985
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otheJWise, without prior permission of the copyright holder.
ISSN
0724-9993
ISBN 978-3-528-08911-5
Preface
In this monograph some stability properties of linear, time-variant, discrete-time systems are summarized, where some properties are well known, some are little-known facts, and a few may be new. Models for this treatise an the asymptotical behaviour of solutions of difference equations are the commonly known excellent books of CESARI [3] and CONTI [5]. In the tables of Chapter 1 the definitions and the essential statements an stability of discrete-time systems are summarized, such that Chapter 2 to 5 may be regarded as explaining appendices for these tables. I am grateful to Paul Ludyk, who typed and corrected the manuscript with great skill and patience, and Alois Ludyk, who drew the figures with great artistic skill.
Bremen, January 1985
Günter Ludyk
Contents
Notations
1
1.Introduction and Summary
4
2.Mathematical Description of Discrete-Time Systems 2.1 State Equations 2.2 Properties of the Transition Matrix 2.3 LAGRANGE-Identity and GREEN's Formula for Difference Equations 2.4 Estimations for the Norm of the Transition Matrix 3.Stability of Free Discrete-Time Systems 3.1 3.2 3.3 3.4 3.5 3.6 3.7
LJAPUNOW- and LAGRANGE-Stability Short Time Boundedness UniformStability Asymptotic Stability ~P-stability
Exponential and Uniform Asymptotic Stabi
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