Solution of positive periodic discrete Lyapunov equations with applications to the balancing of periodic systems

The discrete-time positive periodic Lyapunov equations have important applications in the balancing and potentially also in the model reduction of discrete-time periodic systems. Efficient numerically reliable algorithms based on periodic Schur decomposition are proposed for the solution of these equations. The proposed algorithms are extensions of the method of Hammarling for the case of positive semidefinite solution. Special methods were developed to solve efficiently small order periodic Lyapunov and Sylvester equations.