Periodic solutions of matrix Riccati equations with detectability and stabilizability

Abstract

The matrix Riccati differential equation with periodic coefficients is discussed in this paper. As is well known, such equations are frequently encountered in the applications of the optimal filtering and control theory. The necessary and sufficient condition is derived for the existence of a unique, non-negative definite and periodic solution and the asymptotically stable closed-loop system. Such condition is stated in terms of the stabilizability and detectability of matrix pairs, that is the natural generalization of those for constant matrix pairs.