Algebraic Riccati Equations

Algebraic Riccati equations play a central role in modern control theory and signal processing, essential topics for industrial scientists, engineers, and mathematicians. This book provides a thorough treatment of the theory behind these equations, the solutions arising from continuous and discrete systems, and includes a collection of eight problem areas or applications in which they play a crucial role.

This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions. The second and third parts form the core of the book and concern the solutions of algebraic Riccati equations arising from continuous and discrete systems. The geometric theory and iterative analysis are both developed in detail. The last part of the book is an exciting collection of eight problem areas in which algebraic Riccati equations play a crucial role. These applications range from introductions to the classical linear quadratic regulator problems and the discrete Kalman filter to modern developments in HD*W*w control and total least squares methods.

1 - Preliminaries from the theory of matrices
2 - Indefinite scalar products
3 - Skew-symmetric scalar products
4 - Matrix theory and control
5 - Linear matrix equations
6 - Rational matrix functions
7 - Geometric theory: the complex case
8 - Geometric theory: the real case
9 - Constructive existence and comparison theorems
10 - Hermitian solutions and factorizations of rational matrix functions
11 - Perturbation theory
12 - Geometric theory for the discrete algebraic Riccati equation
13 - Constructive existence and comparison theorems
14 - Perturbation theory for discrete algebraic Riccati equations
15 - Discrete algebraic Riccati equations and matrix pencils
16 - Linear-quadratic regulator problems
17 - The discrete Kalman filter
18 - The total least squares technique
19 - Canonical factorization
20 - Hoo control problems
21 - Contractive rational matrix functions
22 - The matrix sign function
23 - Structured stability radius