Strongly Stabilizable Distributed Parameter Systems

Name: Strongly Stabilizable Distributed Parameter Systems
Brand: SIAM - SOCIETY FOR INDUSTRIAL AND APPLIED
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By: Job Oostveen

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Hardcover | 29 November 2000

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Hardcover
162 Pages

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25.4 x 17.78 x 1.27

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Questions about stability arise in almost every control problem. There are many physical problems in which exponential stability is too strong and for which the concept of strong stability is appropriate. This book provides a solid mathematical framework for a structured approach to strongly stabilizable systems through integration of fundamental theory, physical applications and numerical results. The author incudes a mathematical framework for studying PDE models of large flexible structures, an important class of applications. The author's structured approach focuses on two themes: the development of system theoretic results for strongly stable systems, and the formulation of these results for a class of dissipative systems with collocated actuators and sensors. The tools set forth in this book extend the scope of applicability of PDE control techniques, including the important aspect of numerical approximation. Most importantly, the author justifies all theory by providing physical examples for which the theory is relevant. The book encompasses basic system theoretic notions, such as stability, stabilizability, detectability, coprime factorizations, and control related topics like Riccati equations, LQ optimal control, robust stabilization, nonlinear perturbations and numerical approximation.

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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Dynamics & Statics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Solids Dynamics & Vibration Technology in General Maths for Engineers

Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Science in General Maths for Scientists Applied Mathematics

Preface	p. ix
Notation	p. xi
Introduction	p. 1
Motivation	p. 1
Overview of the Results	p. 5
Two Main Themes	p. 9
Strong Stability	p. 9
Dissipative Systems with Collocated Actuators and Sensors	p. 15
Strong Stabilizability and Strong Detectability	p. 23
Definitions and Motivation	p. 23
Equivalence of Internal and External Stability	p. 24
The Standard LQ Riccati Equation	p. 26
Riccati Equations for Statically Stabilizable Systems	p. 31
Problem Formulation	p. 31
Mathematical Preliminaries	p. 33
Riccati Equations for Stable Systems	p. 39
Riccati Equations for Unstable Systems	p. 42
Special Types of Riccati Equations	p. 44
J-Spectral Factorizations	p. 44
The Strict Positive Real Lemma	p. 46
The Strict Bounded Real Lemma	p. 46
The Coercive LQ Case	p. 47
Examples	p. 49
The Strict Positive Real Lemma	p. 49
The Standard LQ Riccati Equation	p. 49
Numerical Approximation	p. 51
The LQ Riccati Equation for Strongly Stabilizable Systems	p. 51
Approximation of Strongly Stable Systems	p. 55
Approximation of the Strongly Stabilizing Solution	p. 60
Applications to Dissipative Systems with Collocated Actuators and Sensors	p. 62
Coprime Factorizations and Dynamic Stabilization	p. 67
Problem Formulation	p. 67
Coprime Factorizations	p. 69
State-Space Formulas for Normalized Coprime Factorizations	p. 72
Dynamic Stabilization	p. 77
Robust Stabilization	p. 85
The Nehari Problem	p. 85
Parameterization of Robustly Stabilizing Controllers	p. 96
Robustness with Respect to Nonlinear Perturbations	p. 105
Preliminaries	p. 106
The Popov Criterion	p. 107
Proof of the Popov Criterion	p. 108
Asymptotic Tracking	p. 112
Examples of Strongly Stabilizable Systems	p. 115
Boundary Control of a Flexible Beam	p. 115
Boundary Control of a Flexible Plate	p. 117
Propagation of Sound in a Duct	p. 120
A Flexible Structure with Rigid Body Dynamics	p. 129
Conclusions	p. 137
Possibilities for Further Research	p. 138
Bibliography	p. 141
Index	p. 149
Table of Contents provided by Syndetics. All Rights Reserved.

Strongly Stabilizable Distributed Parameter Systems

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Hardcover

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