Large periodic Lyapunov equations: Algorithms and applications

Two algorithms for the solution of discrete-time periodic Lyapunov equations are presented. The first one is a variant of the squared Smith iteration, which is solely based on matrix multiplications and thus attractive to parallel computing environments. The second algorithm is based on Krylov subspaces and employs a recently developed variant of the block Arnoldi algorithm. It is particularly suited for periodic Lyapunov equations with large and sparse coefficient matrices. We also demonstrate how these methods can be applied to balanced truncation model reduction of periodic discrete-time systems and the solution of periodic Riccati equations.