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E-raamat: Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters

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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.

Arvustused

From the reviews:









"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)

1. Introduction 1(6)
1.1 Book Organization
3(4)
2. Linear Time-Varying Systems 7(24)
2.1 Existence and Uniqueness
7(1)
2.2 The State Transition Matrix
8(3)
2.3 Lyapunov Stability of Linear Time-Varying Systems
11(4)
2.4 Sufficient Conditions for Exponential Stability
15(3)
2.5 Input-Output Gain of a Linear Time-Varying System
18(5)
2.6 Discrete-Time Systems
23(4)
2.6.1 Lyapunov Stability of Discrete-Time Systems
25(2)
Summary
27(1)
Exercises
28(3)
3. Quadratic Stability 31(62)
3.1 Necessary and Sufficient Conditions for Quadratic Stability
31(14)
3.1.1 Polytopic Systems
43(2)
3.2 The General Nonlinear Parameter Dependence Case
45(13)
3.2.1 Polynomial Dependence on Parameters
45(1)
3.2.2 The Polytopic Covering Technique
46(12)
3.3 Other Approaches for Quadratic Stability Analysis
58(5)
3.3.1 Gridding
58(1)
3.3.2 A Statistical Approach
59(3)
3.3.3 A Comparison Between the Various Methods for Quadratic Stability Analysis
62(1)
3.4 Quadratic Stability and Performances
63(7)
3.4.1 Quadratic Stability and Pole Placement (Quadratic D-Stability)
63(3)
3.4.2 Quadratic L2 Performance
66(2)
3.4.3 Quadratic Guaranteed Cost
68(2)
3.5 Norm Bounded Uncertainties
70(14)
3.5.1 The Multi-Block Case
75(3)
3.5.2 Quadratic Stability and Performances
78(6)
3.6 Connections between Quadratic Stability and 7-G, Control
84(5)
Summary
89(2)
Exercises
91(2)
4. Systems Depending on Bounded Rate Uncertainties 93(20)
4.1 Quadratic Stability via Parameter Dependent Lyapunov Functions
93(2)
4.2 Multi-Affine Quadratic Stability
95(4)
4.3 Polynomial Quadratic Stability
99(3)
4.4 A More General Class of Parameter Dependent Lyapunov Functions
102(6)
Summary
108(2)
Exercises
110(3)
5. Controller Design 113(38)
5.1 Quadratic Stabilization
113(13)
5.1.1 Quadratic Stabilization via State Feedback
113(2)
5.1.2 Quadratic Stabilization via Output Feedback
115(11)
5.2 Quadratic Stabilization with Performances
126(8)
5.2.1 Quadratic D-Stabilization
126(4)
5.2.2 Quadratic r2 Performance Control
130(3)
5.2.3 Guaranteed Cost Control
133(1)
5.3 Robust Stabilization in the Presence of Bounded Rate Parameters
134(2)
5.4 Systems Depending on Norm Bounded Uncertainties
136(11)
5.4.1 Quadratic Stabilization
136(4)
5.4.2 Quadratic Stabilization and Performances
140(7)
Summary
147(2)
Exercises
149(2)
6. Discrete-Time Systems 151(22)
6.1 Quadratic Stability
151(4)
6.1.1 Parametric Uncertainties
151(2)
6.1.2 Norm Bounded Uncertainties
153(1)
6.1.3 Connections Between Quadratic Stability and Hinfinity Control
154(1)
6.2 Systems Subject to Bounded Rate Parameters
155(4)
6.2.1 Connections with the Quadratic Stability Approach
159(1)
6.3 A Real World Example: Control of a Plasma Wind Tunnel
159(7)
6.3.1 Controller Design
161(1)
6.3.2 Implementation Aspects and Numerical Results
162(4)
6.4 Quadratic Stabilization
166(3)
6.4.1 Parametric Uncertainties
166(2)
6.4.2 Norm Bounded Uncertainties
168(1)
Summary
169(2)
Exercises
171(2)
A. Appendix 173(12)
A.1 Definite Matrix Sets
173(2)
A.2 Kronecker Product and Sum
175(1)
A.3 The Lyapunov Equation
176(3)
A.3.1 Some Useful Inequalities
177(1)
A.3.2 Discrete-Time Lyapunov Equation
177(2)
A.4 Shur Complements
179(6)
References 185(10)
Index 195