Periodic Lyapunov equations: Some applications and new algorithms

The discrete-time periodic Lyapunov equation has several important applications in the analysis and design of linear periodic control systems. Specific applications considered are the solution of state- and output-feedback optimal periodic control problems, the stabilization by periodic state feedback and the square-root balancing of discrete-time periodic systems. Efficient and numerically reliable algorithms based on the periodic Schur decomposition are proposed for the solution of periodic Lyapunov equations. The proposed algorithms are extensions of the direct solution methods for standard discrete-time Lyapunov equations for the case of indefinite as well as non-negative definite solution.