Solving Ill-Conditioned Matrix Equations in Control
Final technical rept. 15 Jun 1991-14 Oct 1993
CALIFORNIA UNIV SANTA BARBARA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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The primary objective of this grant has been the study of algorithms for solving ill-conditioned matrix equations arising in control, filtering, and system theory. Much of our work has concentrated on matrix Riccati and Lyapunov equations which are absolutely fundamental to the field. We have made significant advances on a number of fronts in the numerical solution of large- scale and ill-conditioned Lyapunov, Sylvester, and Riccati equations. Substantial progress has been made in other areas as well, including a new family of algorithms based on matrix interpolation for frequency response and related problems, a number of key advances in numerical linear algebra, algorithms for infinite-dimensional systems, a new theory of small sample statistical condition estimation, and software implementations of many of our algorithms. Our results have been reported in over thirty scholarly articles. Computational control, Matrix equations, Numerical linear algebra, Ill conditioning.
- Operations Research