Algebraic Riccati Equations

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Clarendon Press, Sep 7, 1995 - Mathematics - 498 pages
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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.
 

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Contents

MATRIX THEORY
1
INDEFINITE SCALAR PRODUCTS
31
SKEWSYMMETRIC SCALAR PRODUCTS
71
MATRIX THEORY AND CONTROL
83
LINEAR MATRIX EQUATIONS
97
RATIONAL MATRIX FUNCTIONS
107
CONTINUOUS ALGEBRAIC RICCATI
147
THE REAL CASE
215
PERTURBATION THEORY FOR DISCRETE
329
APPLICATIONS AND CONNECTIONS
347
THE DISCRETE KALMAN FILTER
371
THE TOTAL LEAST SQUARES TECHNIQUE
387
CANONICAL FACTORIZATION
397
H CONTROL PROBLEMS
409
CONTRACTIVE RATIONAL
421
THE MATRIX SIGN FUNCTION
437

CONSTRUCTIVE EXISTENCE AND COMPARISON
231
HERMITIAN SOLUTIONS AND FACTORIZATIONS
247
PERTURBATION THEORY
257
DISCRETE ALGEBRAIC
269
CONSTRUCTIVE EXISTENCE AND COMPARISON
307
STRUCTURED STABILITY RADIUS
447
BIBLIOGRAPHY
459
LIST OF NOTATION AND CONVENTIONS
473
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