A SIMPLE STATE-SPACE APPROACH TO SPECTRAL FACTORIZATION FOR DISCRETE-TIME SYSTEM

This paper is concerned with inner-outer/spectral factorizations appearing in discrete-time H-2 / H(infinity) optimal controls. We derive an algorithm for the inner-outer factorization of a stable transfer matrix, using the compact notation for the state-space representation of rational transfer matrices and the Schur decomposition of an associated symplectic matrix. The same technique is also employed for developing an algorithm of spectral factorization appearing in H(infinity) controls. Moreover, we extend the spectral factorization result to the case where the original transfer matrix is not necessarily stable. A numerical result is included.