Stability of Time-Variant Discrete-Time Systems

Günter Ludyk

ISBN 10: 3528089113 / ISBN 13: 9783528089115

Editore: Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1985, 1985

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 160 pp. Deutsch.

Codice articolo 9783528089115

Dati bibliografici

• Titolo: Stability of Time-Variant Discrete-Time Systems
• Editore: Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1985
• Data di pubblicazione: 1985
• Lingua: Tedesco
• ISBN 10: 3528089113
• ISBN 13: 9783528089115
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 9 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 9 millimetri di profondità
• Peso: 254 grammi

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Riassunto

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.

Contenuti

1.Introduction and Summary.- 2.Mathematical Description of Discrete-Time Systems.- 3.Stability of Free Discrete-Time Systems.- 4.Stability of Forced Discrete-Time Systems.- 5.Relations between Internal and External Stability.- References.