Existence condition of positive-definite solutions for algebraic matrix Riccati equations (Q1821731)

Algebraic matrix Riccati equations are considered which arise in the optimal filtering as well as in control problems of continuous time-invariant systems. A necessary and sufficient condition is established for the existence of unique positive-definite solutions and the asymptotically stable closed-loop system. The condition is stated in terms of the detectability and stabilizability of certain matrix pairs, as was the case for the non-negative-definite solution. Simple examples are included to illustrate the new results against the existing ones.