Perturbation Analysis of the Continuous and Discrete Matrix Riccati Equations

This paper presents a complete perturbation analysis of the continuous and discrete matrix algebraic equations in the theory of linear-quadratic optimization. In particular the conditioning of the corresponding Riccati equations is studied. The obtained estimates are non-local since they are valid for perturbations which are not asymptotically small. They may be used for investigating the numerical performance of the existing computational algorithms for Riccati equations in the presence of rounding errors.