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Robust Stability and Convexity : An Introduction : Advances in Industrial Control - Jacob Kogan

Robust Stability and Convexity : An Introduction

Advances in Industrial Control

Paperback

Published: January 1994
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A fundamental problem in control theory is the stability of a given linear system. The design of a control system is generally based on a simplified model. The true values of the physical parameters may differ from the assumed values. This monograph addresses stability problems for linear systems with parametric uncertainty. The application of convexity techniques leads to computationally tractable stability criteria for families of characteristic functions with nonlinear dependence on the parameters. Stability results as well as stability criteria for time-delay systems with uncertainties in coefficients and delays are reported.

Introduction and Motivationp. 1
Illustrationp. 1
Stability and Convexityp. 2
Stability of Box Polynomial Familiesp. 7
Kharitonov's Theoremp. 7
Other root location regions: [Omega] stabilityp. 10
Principal Vertices and Stabilityp. 11
Principal Directions and Principal Verticesp. 13
Principal Vertices and Testing Familyp. 18
Examples: Schur, Hurwitz, and Sector Stabilityp. 20
Hurwitz Stability of Weighted Diamondsp. 23
Extreme Point Resultsp. 29
Stability Radii and Convex Analysisp. 37
Stability Radii and Degree Droppingp. 38
Constrained Optimization Problemp. 44
Complex Stability Radiusp. 44
Stability Radiusp. 46
Examples: Stability Radii for Schur and Hurwitz Polynomialsp. 49
Real Stability Radius: Examplesp. 52
Link to Structured Matrix Perturbationsp. 55
Matrix Perturbationsp. 56
Multiple Matrix Perturbations and [mu]p. 60
Multiaffine Polynomial Familiesp. 63
Orientation Preserving Multiaffine Transformationp. 65
Image of a Box Under Multiaffine Transformationp. 73
Robust Stability of Multiaffine Polynomial Familiesp. 75
Cascade of Uncertain Blocksp. 76
Interval Plants with Interval Controllersp. 84
Numerical Examplep. 93
Multidimensional Systems and Systems with Commensurate Delaysp. 99
Stability of linear systems and zeros of characteristic polynomialsp. 100
Stability of a Bivariate Polynomialp. 102
Stability Radiusp. 103
Reduction to the Polynomial Problemp. 104
Evaluation of Stability Radiusp. 107
Example: Hurwitz Stability of Interval Bivariate Polynomialsp. 109
Quasipolynomials with Commensurate Delays and Zero Exclusion Criterionp. 110
Diamond Quasipolynomials: Eight Edges Theoremp. 113
Uncertain Time-Delay Systemsp. 117
Time-Delay Systems and Zero Exclusion Criterionp. 118
Real Interval Quasipolynomialsp. 121
Kharitonov Rectangles and Robust Stability Conditionsp. 121
Image of a Box Under Nonlinear Mappingp. 124
Principal Segmentsp. 127
Numerical Examplep. 129
Eight Edges Theoremp. 131
Convexity of Frequency Response Arcs Associated with Hurwitz Quasipolynomialsp. 137
Convexity for Entire Functionsp. 138
Angular Derivative Formalismp. 144
Computation of Angular Derivativesp. 146
Inner Frequency Response Setp. 148
Epiloguep. 153
Lyapunov Criterionp. 154
Simultaneous Stabilizationp. 155
Bibliographyp. 157
List of Special Symbolsp. 170
Author Indexp. 172
Subject Indexp. 175
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540199199
ISBN-10: 3540199195
Series: Advances in Industrial Control
Audience: General
Format: Paperback
Language: English
Number Of Pages: 180
Published: January 1994
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: GB
Dimensions (cm): 23.39 x 15.6  x 1.07
Weight (kg): 0.28