Lecture Notes in Control and Information Sciences

By: Francesco Amato

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Paperback | 21 February 2006

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The last thirty years have witnessed an enormous e?ort in the ?eld of robust control of dynamical systems. The main objective of this book is that of presenting,inauni?edframework,themainresultsappearedintheliterature on this topic, with particular reference to the robust stability problem for linear systems subject to time-varying uncertainties. Thebookmainly focuseson thoseproblems for which ade?nitive solution has been found; indeed most of the results we shall present are given in the form of necessary and su?cient conditions involving the feasibility of Linear Matrix Inequalities based problems. For self-containedness purposes, most of the results provided in the book areproven.Wehavetriedtomaintainthedevelopmentoftheproofsassimple as possible, without sacri?cing the mathematical rigor. Some parts of the book (especially those contained in Chaps. 2, 3 and 5) can be teached in advanced control courses; however this work is mainly devoted to both researchers in the ?eld of systems and control theory and engineers working in industries which want to apply the methodologies p- sentedinthebooktopracticalcontrolproblems.Tothisregard,asthevarious resultsarederived,theyareimmediatelyreinforcedwithrealworldexamples.

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"This book provides a systematic treatment of the theory of robust control of dynamical systems. ... The author has chosen to consider only the problems for which a definitive solution has been found, having in mind researchers or engineers working in industries who want to apply these methodologies to practical control problems. ... The presentation is self contained, all proofs are given as well as real world examples. ... The self contained presentation makes it suitable to be used for educational post-graduate purposes." (Anna Maria Perdon, Zentralblatt MATH, Vol. 1142, 2008)

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Introduction	p. 1
Book Organization	p. 3
Linear Time-Varying Systems	p. 7
Existence and Uniqueness	p. 7
The State Transition Matrix	p. 8
Lyapunov Stability of Linear Time-Varying Systems	p. 11
Sufficient Conditions for Exponential Stability	p. 15
Input-Output Gain of a Linear Time-Varying System	p. 18
Discrete-Time Systems	p. 23
Lyapunov Stability of Discrete-Time Systems	p. 25
Summary	p. 27
Exercises	p. 28
Quadratic Stability	p. 31
Necessary and Sufficient Conditions for Quadratic Stability	p. 31
Polytopic Systems	p. 43
The General Nonlinear Parameter Dependence Case	p. 45
Polynomial Dependence on Parameters	p. 45
The Polytopic Covering Technique	p. 46
Other Approaches for Quadratic Stability Analysis	p. 58
Gridding	p. 58
A Statistical Approach	p. 59
A Comparison Between the Various Methods for Quadratic Stability Analysis	p. 62
Quadratic Stability and Performances	p. 63
Quadratic Stability and Pole Placement (Quadratic D-Stability)	p. 63
Quadratic L[subscript 2] Performance	p. 66
Quadratic Guaranteed Cost	p. 68
Norm Bounded Uncertainties	p. 70
The Multi-Block Case	p. 75
Quadratic Stability and Performances	p. 78
Connections between Quadratic Stability and H[infinity] Control	p. 84
Summary	p. 89
Exercises	p. 91
Systems Depending on Bounded Rate Uncertainties	p. 93
Quadratic Stability via Parameter Dependent Lyapunov Functions	p. 93
Multi-Affine Quadratic Stability	p. 95
Polynomial Quadratic Stability	p. 99
A More General Class of Parameter Dependent Lyapunov Functions	p. 102
Summary	p. 108
Exercises	p. 110
Controller Design	p. 113
Quadratic Stabilization	p. 113
Quadratic Stabilization via State Feedback	p. 113
Quadratic Stabilization via Output Feedback	p. 115
Quadratic Stabilization with Performances	p. 126
Quadratic D-Stabilization	p. 126
Quadratic L[subscript 2] Performance Control	p. 130
Guaranteed Cost Control	p. 133
Robust Stabilization in the Presence of Bounded Rate Parameters	p. 134
Systems Depending on Norm Bounded Uncertainties	p. 136
Quadratic Stabilization	p. 136
Quadratic Stabilization and Performances	p. 140
Summary	p. 147
Exercises	p. 149
Discrete-Time Systems	p. 151
Quadratic Stability	p. 151
Parametric Uncertainties	p. 151
Norm Bounded Uncertainties	p. 153
Connections Between Quadratic Stability and H[infinity] Control	p. 154
Systems Subject to Bounded Rate Parameters	p. 155
Connections with the Quadratic Stability Approach	p. 159
A Real World Example: Control of a Plasma Wind Tunnel	p. 159
Controller Design	p. 161
Implementation Aspects and Numerical Results	p. 162
Quadratic Stabilization	p. 166
Parametric Uncertainties	p. 166
Norm Bounded Uncertainties	p. 168
Summary	p. 169
Exercises	p. 171
Appendix	p. 173
Definite Matrix Sets	p. 173
Kronecker Product and Sum	p. 175
The Lyapunov Equation	p. 176
Some Useful Inequalities	p. 177
Discrete-Time Lyapunov Equation	p. 177
Shur Complements	p. 179
References	p. 185
Index	p. 195
Table of Contents provided by Ingram. All Rights Reserved.

Lecture Notes in Control and Information Sciences

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