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E-raamat: A Unified Algebraic Approach To Control Design

(University of California, La Jolla, California, USA), (Tokyo Institute of Technology, Japan),
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This text deals with the most fundamental deficiency of modern theory control: the lack of an easily applicable method for the design of low order controllers. It shows that solutions to many different problems in control all reduce to the same linear algebra problem. It employs matrix equalities and matrix inequalities in the solutions of fixed order control and also provides computational algorithms.
Series Introduction xi
Preface xiii
Introduction
1(10)
Output Performance and Second-Order Information
2(1)
Stability, Pole Locations and Second-Order Information
3(1)
Stability Robustness and Second-Order Information
4(1)
Disturbance Attenuation and Second-Order Information
5(1)
Stability Margins Measured by H∞ Norms
6(1)
Computational Errors
7(4)
Chapter 1 Summary
9(2)
Linear Algebra Review
11(22)
Singular Value Decomposition
12(1)
Moore-Penrose Inverse
13(1)
Solutions of Selected Linear Algebra Problems
14(19)
Chapter 2 Summary
32(1)
Analysis of First-Order Information
33(18)
Solutions of Linear Differential Equations
33(2)
Solutions of Linear Difference Equations
35(1)
Controllability and Observability of Continuous-Time Systems
35(6)
Controllability and Observability of Discrete-Time Systems
41(4)
Lyapunov Stability of Linear Systems
45(6)
Chapter 3 Summary
49(2)
Second-Order Information in Linear Systems
51(38)
The Deterministic Covariance Matrix for Continuous-Time Systems
51(3)
Models for Control Design (Continuous-Time)
54(1)
Stochastic Interpretations
55(2)
The Discrete System D-Covariance
57(2)
Models for Control Design (Discrete-Time)
59(2)
System Performance Analysis
61(13)
Robust Stability and Performance Analysis
74(15)
Chapter 4 Summary
88(1)
Covariance Controllers
89(42)
Covariance Control Problem
89(1)
Continuous-Time Covariance Controllers
90(25)
Discrete-Time Covariance Controllers
115(5)
Minimal Energy Covariance Control
120(5)
Finite Wordlength Covariance Control
125(1)
Synchronous Sampling
125(2)
Skewed Sampling
127(1)
Covariance Assignment
128(3)
Chapter 5 Summary
129(2)
Covariance Upper Bound Controllers
131(26)
Covariance Bounding Control Problem
131(2)
Continuous-Time Case
133(13)
Discrete-Time Case
146(11)
Chapter 6 Summary
156(1)
H∞ Controllers
157(18)
H∞ Control Problem
157(1)
Continuous-Time Case
158(10)
Discrete-Time Case
168(7)
Chapter 7 Summary
174(1)
Model Reduction
175(14)
H∞ Model Reduction
175(7)
Model Reduction with Covariance Error Bounds
182(7)
Chapter 8 Summary
188(1)
Unified Perspective
189(16)
Continuous-Time Case
190(7)
Discrete-Time Case
197(8)
Chapter 9 Summary
204(1)
Projection Methods
205(24)
Alternating Convex Projection Techniques
205(8)
Geometric Formulation of Covariance Control
213(4)
Projections for Covariance Control
217(4)
Geometric Formulation of LMI Control Design
221(4)
Fixed-Order Control Design
225(4)
Chapter 10 Summary
228(1)
Successive Centering Methods
229(24)
Control Design with Unspecified Controller Order
229(6)
Control Design with Fixed Controller Order
235(11)
Control Design with Fixed Controller Structure
246(7)
Chapter 11 Summary
251(2)
A Linear Algebra Basics 253(14)
Partitioned Matrices
253(1)
Sign Definiteness of Matrices
254(2)
A Linear Vector Space
256(1)
Fundamental Subspaces of Matrix Theory
257(7)
Convex Sets
264(1)
Matrix Inner Products and the Projection Theorem
265(2)
B Calculus of Vectors and Matrices 267(6)
Vectors
267(1)
Matrices
268(5)
C Balanced Model Reduction 273(2)
References 275(8)
Index 283
Dimitri E. Grigoriadis
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