A note on periodic Lyapunov equations

Periodic Lyapunov differential equations are studied arising in stability analysis of linear periodic systems. Existence conditions of periodic solution, its nonsingularity and sign-definiteness are established in connection with the stability, observability and detectability of systems. The results are useful not only for stability analysis but for periodic Riccati equations in H/sub /spl infin// control problems, robust stabilization problems, and so forth. A condition is also derived for a class of periodic systems perturbed by nonperiodic terms to be quadratically stable.