鲁棒控制理论教程

Series Preface

Preface

Figures

0 Introduction

0.1 System representations

0.1.1 Block diagrams

0.1.2 Nonlinear equations and linear decompositions

0.2 R,obust control problems and uncertainty

0.2.1 Stabilization

0.2.2 Disturbances and commands

0.2.3 Unmodeled dynamics

Notes and references

1 Preliminaries in Finite Dimensional Space

1.1 Linear spaces and mappings

1.1.1 Vector spaces

1.1.2 Subspaces

1.1.3 Bases, 8pans, and linear independence

1.1.4 Mappings and matrix representations

1.1.5 Change of basis and invariance

1.2 Subsets and convexity

1.2.1 Some basic topology

1.2.2 Convex sets

1.3 Matrixtheory

1.3.1 Eigenvalues and Jordan form

1.3.2 Self-adjoint, unitary, and positive definite matrices

1.3.3 Singular value decomposition

1.4 Linear matrix inequalities

Exercises

Notes and references

2 State Space System Theory

2.1 The autonomous system

2.2 Controllability

2.2.1 Reachability

2.2.2 Properties of controllability

2.2.3 Stabilizability...

2.2 ,4 Controllability from a single input

2.3 Eigenvalue assignment

2.3.1 Single-input case

2.3.2 Multi-input case

2.4 Observability...

2,4.1 The unobservable subspace

2.4.2 Observers

2.4.3 Observer-based Controllers

2.5 Minimal realizations

2.6 Transfer functions and state space

2.6.1 R,ational matrices and state space realizations

2.6.2 Minimality

Exercises

Notes and references

3 Linear Analysis

3.1 Normed and inner product spaces

3.1 ,1 Complete spaces

3.2 Operators

3.2.1 Banach algebras

3.2.2 Some elements of spectral theory

3.2.3 Adjoint operators in Hilbert space

3.3 Frequency domain spaces: Signals

3.3.1 The space /2 and the Fourier transform

3.3.2 The spaces H2 and H21 and the Laplace transform

3.3.3 Summarizing the big picture

3.4 Frequency domain spaces: Operators

3.4.1 Time invariance and multiplication operators

3.4.2 Causality with time invariance

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The text is written to comprise a two-quarter or two-semester graduate course in applied mathematics or engineering. Alternatively, for students with background in state space methods, a serious approach at a significant portion of the material can be achieved in one semester. The material has been successfully taught in this capacity during the past few years by the authors at Caltech, University of Waterloo, University of Illinois, and UCLA. Students are assumed to have some familiarity with linear algebra, and otherwise only advanced calculus and basic complex analysis are strictly required. The presentation style assumes, however, a mathematically inclined reader, since we focus on a complete theoreticaJ foundation rather than on application examples.