A Unified Algebraic Approach To Control Design

by Skelton; Robert E.

• ISBN13: 9780748405923
• ISBN10: 0748405925
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-10-17
• Publisher: CRC Press

Summary

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.

Table of Contents

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