Stability and Stable Oscillations in Discrete Time Systems,9789056996710

Stability and Stable Oscillations in Discrete Time Systems

by ;
ISBN13: 9789056996710
ISBN10: 9056996711
Format: Hardcover
Pub. Date: 2000-10-31
Publisher(s): CRC Press
List Price: $155.15

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Summary

The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in engineering such as stability of digital filters, digitally controlled thermal processes, neurodynamics, and chemical kinetics. This book will be an invaluable reference source for those whose work is in the area of discrete dynamical systems, difference equations, and control theory or applied areas that use discrete time models.

Author Biography

Aristide Halanay received his PhD from Moscow University and was a professor in the Department of Mathematics at Bucharest University Vladimir Rasvan received his PhD in electrical engineering from Bucharest Technical University. He is a professor in the Department of Automatic Control at Craiova University

Table of Contents

Series Editors' Preface xi
Preface xiii
Introduction
1(20)
Models with Discrete Storage of the Information
2(5)
Discrete Time Models Induced by the Impulses Occurring in Continuous-Time Systems
7(6)
Discrete Systems Occurring from Sampled Data Control Systems
13(3)
Numerical Treatment of Continuous-Time Systems
16(3)
About the Book
19(2)
Stability Theory
21(98)
Linear Discrete Time Systems with Constant Coefficients
21(16)
A stability criterion
25(1)
Example: stability of a digital filter
26(2)
Example: inherent stability of a digitally controlled thermal process
28(1)
The Liapunov matrix equation for the discrete case
29(3)
Robust stability and stability radii
32(5)
General Properties of Linear Systems
37(6)
Stability by the First Approximation
43(7)
A preliminary result
44(1)
Stability of equilibria for time-invariant systems
44(3)
Stability of motion for time varying systems
47(3)
Linear Discrete-Time Systems with Periodic Coefficients
50(10)
Multipliers and structure of solutions
50(4)
Stability results
54(6)
Liapunov Functions
60(19)
Stability concepts
60(2)
Stability via Liapunov functions
62(5)
Liapunov functions for linear systems. Exponential stability
67(7)
Stability under perturbations
74(5)
Invariance Principle. Barbashin-Krasovskii-La Salle Theorem
79(5)
Discrete dynamical systems
79(3)
The invariance principle
82(2)
Stability in Discrete Models of Chemical Kinetics
84(8)
Stability Results in Neurodynamics
92(7)
Stability via Input/Output Properties
99(20)
The Perron Condition
99(3)
Dissipativity and stability
102(11)
Stabilization of bilinear systems
113(6)
Absolute Stability of Control Systems
119(102)
The Simplest Absolute Stability Criterion of Tsypkin
123(12)
Quadratic Constraints of Yakubovich Type
135(5)
An Absolute Stability Criterion for the Case of Nondecreasing Nonlinear Functions
140(3)
The Brockett-Willems Type Criterion for Systems with Nondecreasing Nonliearity
143(10)
Liapunov Functions and Frequency Domain Inequalities in Absolute Stability. The KSPY Lemma (Single-Input Case)
153(16)
For and against Liapunov functions in the study of nonlinear systems
153(2)
The Lemma for discrete systems
155(2)
Problem statement
157(2)
Proof of the lemma - the stable case
159(9)
Proof of the lemma - the general case
168(1)
A New Condition of Absolute Stability for Systems with Slope Restricted Nonlinearity
169(15)
System description. The class of nonlinearities. The associated system and the first integral
171(2)
The stability criterion
173(8)
An example
181(3)
Concluding remarks
184(1)
The KSPY Lemma (Multi-Input Case)
184(19)
Weak and strong frequency domain conditions
185(1)
An abstract minimization problem
186(3)
A linear quadratic minimization problem
189(5)
The KSPY lemma under the strong frequency domain inequality
194(6)
The KSPY lemma under the weak frequency domain inequality
200(3)
Applications of the Multi-Input KSPY Lemma
203(18)
Linear feedback disturbance attenuation
203(6)
A small gain result
209(1)
Absolute stability for systems with several sector and slope restricted nonlinearities
210(11)
Stable Oscillations
221(46)
Periodic Solutions of Forced Linear Systems with Periodic Coeffcients (Forced Oscillations)
221(6)
Almost Periodic Sequences
227(12)
Motivation
228(1)
Standard theory of almost periodic sequences
229(5)
A new Bochner theory for almost periodic sequences
234(1)
Asymptotic almost periodic sequences
235(4)
Almost Periodic Linear Oscillations
239(10)
Periodic and Almost Periodic Oscillations in Nonlinear Systems
249(7)
Periodic oscillations
249(4)
Almost periodic oscillations
253(3)
Averaging
256(11)
References 267(12)
Index 279

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