An extended symplectic pencil approach to the optimal H(infinity)problem

Explicit state space formulas for the non-canonical spectral factorization of a para-Hermitian rational matrix function, which cannot be solved by using a Riccati equation, are constructed based on the ESP method in discrete time. The explicit indivisible criterion is given as means of the factorization using the ESP method. The derived centre factor satisfies the indivisible condition. The results are also verified by a simple numerical example.