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Klappentext 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. Zusammenfassung This monograph provides a treatment of the theory of algebraic Riccati equations, an area of increasing interest in the mathematics and engineering communities. A range of applications are covered, demonstrating the use of these equations for providing solutions to complex problems. Inhaltsverzeichnis 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 Bibliography List of notations Index
