Department of Computing Science
S-901 87 Umeå , Sweden
Consider the continuous-time Riccati equation (CARE)
The central question of forward perturbation analysis for an ARE is: How does the symmetric p.s.d. solution change when the coefficient matrices are subject to perturbations? The central question of backward perturbation analysis for an ARE is: Is an computed symmetric p.s.d. solution of an ARE the exact solution of a slightly perturbed ARE? The interest in these topics is motivated by the fact that each ARE is usually subject to perturbations in the coefficient matrices reflecting various errors in the formulation of the problem and in its solution by a computer. In this talk, we present a unifying framework and effective techniques for creating perturbation theory for AREs, and present improved perturbation results which include perturbation bounds, condition numbers, backward errors, and residual bounds for AREs. The theoretical results are illustrated by numerical examples.