On solving periodic differential matrix equations with applications to periodic system norms computation

Periodic Lyapunov, Sylvester and Riccati differential equations have many important applications in the analysis and design of linear periodic control systems. For the numerical solution of these equations efficient numerically reliable algorithms based on the periodic Schur decomposition are proposed. The new multi-shot type algorithms compute periodic solutions in an arbitrary number of time moments within one period by employing suitable discretizations of the continuous-time problems. In contrast to traditionally used one-shot periodic generator methods, the multi-shot type methods have the advantage to be able to address problems with large periods and/or unstable dynamics. Applications of the proposed techniques to compute several system norms are presented.