Advances in Control Systems and Signal Processing

Stability of Time-Variant Discrete-Time Systems

Authors: Ludyk, Günter

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About this book

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 asymp­ totical 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 essen­ tial 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. Günter Ludyk Bremen, January 1985 Contents Notations 1 1. Introduction and Summary 4 2. Mathematical Description of Discrete-Time Systems 16 2. 1 State Equations 16 2. 2 Properties of the Transition Matrix 19 2. 3 LAGRANGE-Identity and GREEN's Formula for Difference Equations 20 2. 4 Estimations for the Norm of the Transition Matrix 21 3. Stability of Free Discrete-Time Systems 34 3. 1 LJAPUNOW- and LAGRANGE-Stability 34 3. 2 Short Time Boundedness 40 3. 3 UniformStability 45 3. 4 Asymptotic Stability 63 3. 5 ~P-stability 70 3. 6 Exponential and Uniform Asymptotic Stability 75 3. 7 Relations between the Stability Glasses 84 4. Stability of Forced Discrete-Time Systems 86 4. 1 Preliminary Results 86 4. 2 Input-State Stability 93 4.

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Buy this book

eBook $49.99 net
( price for USA )
  • ISBN 978-3-663-13932-4
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $69.99 net
( price for USA )
  • ISBN 978-3-528-08911-5
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Stability of Time-Variant Discrete-Time Systems
Series Title
Advances in Control Systems and Signal Processing
Series Volume
5
Copyright
1985
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Springer Fachmedien Wiesbaden
eBook ISBN
978-3-663-13932-4
DOI
10.1007/978-3-663-13932-4
Softcover ISBN
978-3-528-08911-5
Edition Number
1
Topics