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Contents 1 A Course in Robust Control Theory 1.1 About this book: 1.2 Table of Contents: 2 Control of Uncertain Sampled-Data Systems 2.1 About this book: 2.2 Table of Contents:

[edit] A Course in Robust Control Theory A Convex Approach Series: Texts in Applied Mathematics, Vol. 36 Geir E. Dullerud, University of Illinois, Urbana IL Fernando Paganini, University of California, Los Angeles, CA

About this book:

Robust control theory has been one of the most active areas of mainstream systems theory since the late 1970s. This research activity has been at the confluence of dynamical systems theory, functional analysis, matrix analysis, numerical methods, complexity theory, and engineering applications. The discipline has involved interactions between diverse research groups including pure mathematicians, applied mathematicians, computer scientists, and engineers. A rather extensive set of approaches using a wide variety of mathematical techniques has been produced by the research effort, and applications of robust control theory are spreading to areas as diverse as aerospace systems, chemical processes, power networks, and control of fluids. During the 1990s the theory has seen major advances and achieved a new maturity, centered around convex analysis and optimization.

The goal of this book is to give a graduate-level course on robust control theory that emphasizes these new developments, but at the same time conveys the main principles and ubiquitous tools at the heart of the subject. Its pedagogical objectives are to introduce a coherent and unified framework for studying robust control theory, to provide students with the control-theoretic background required to read andb contribute to the research literature, and to present the main ideas and demonstrations of the major results of robust control theory.

The book will be of value to mathematical researchers and computer scientists wishing to learn about robust control theory, graduate students planning to do research in the area, and engineers interested in the basis of advanced control techniques.

Table of Contents:

Introduction

1. Preliminaries in Finite Dimensional Space
2. State Space System Theory
3. Linear Analysis
4. Model Realizations and Reduction
5. Stabilizing Controllers
6. H2 Optimal Control
7. H_ Synthesis
8. Uncertain Systems
9. Feedback Control of Uncertain Systems
10. Further Topics: Analysis
11. Further Topics: Synthesis Appendices Notation References Index

Control of Uncertain Sampled-Data Systems

Geir E. Dullerud, University of Illinois, Urbana IL

About this book:

Hybrid systems are formed when continuous and discrete-time systems are interconnected. The author?s goal in this book is to provide a detailed treatment of uncertainty analysis for sampled-data hybrid systems in the context of robust control theory. The book has a general scope in that it offers a widely applicable and unifying viewpoint that considers a large class of structured uncertainty problems arising in control, whether the system be hybrid, discrete-time or continuous-time.

In the body of the text, operator theoretic tools and techniques are developed to address the central design issues of performance and stabilization in the presence of structured uncertainty classes. The methods are applied to exact analysis of hybrid sampled-data systems in the H-infinity or Hilbert space setting, with the focus being u-theory and its generalizations to time-varying uncertainty structures. The mathematical machinery and framework presented provide a unified approach to studying performance and uncertainty, and is applicable to both standard and sampled-data systems.

The material of the book is of both theoretical and engineering interest: from a theory perspective the reader can expect to gain intuitive and powerful techniques for treating robust performance problems; practitioners may obtain methods that can be directly implemented in engineering applications. 3

Table of Contents:

1. Introduction
   1. Modelling and Uncertainty
   2. Summary of Contents
2. Preliminaries
   1. Hilbert Space and Banach Algebras
   2. Operator theory
   3. Analytic Functions
   4. Time Domain Spaces and Lifting
   5. Frequency Domain Function Spaces
   6. The Structured Singular Value
3. Uncertain Sampled-data Systems
   1. Summary
4. Analysis of LTI Uncertainty
   1. Converting to Frequency Domain
   2. Destabilizing Perturbations
   3. Robustness Test
   4. Sampled-data Frequency Response
   5. Summary
5. A Computational Framework
   1. Lower Bounds
   2. Upper Bounds
      1. Convergence
      2. Characterization in Finite Dimensions
      3. Evaluating Mn
   3. An Algorithm
   4. Example
   5. Summary
6. Robust Performance
   1. Robust Performance Conditions
      1. Periodic Perturbations
      2. Quasi-Periodic Perturbations
      3. Arbitrary Time-Varying Uncertainty
   2. Computational Tools
      1. Definition and Properties
      2. Reduction to Finite Dimensions
   3. Example Algorithm
      1. A Cutting Plane Approach
      2. Numerical Example
   4. Minimizing the Scaled Hilbert-Schmidt Norm
      1. The Hilbert-Schmidt Norm
      2. Scaling the Hibert-Schmidt Norm and Osborne?s Method
   5. Summary

A. State Space for M

B. Proof of Proposition 5.4

C. State space for Mn

D. State space for Section 6.2

E. Proof of Lemma 6.10

F. The Hilbert-Schmidt Norm of EkM El

G. The S-Procedure