The observability gramian of the observer form and the Schur-Cohn matrix

Abstract

The observer form is a standard minimal realization of the transfer-function matrix G based on an irreducible left matrix-fraction description G = U -1V . It is shown that (in the case of stable G ) there is a simple closed-form expression for the observability gramian of this realization in term of the polynomial matrix U and its ‘reflection’: in fact, gramian is the inverse of the schur-cohn of U .