Balanced minimal realization via singular value decomposition of Sarason operator

In this paper, a method is proposed to obtain a balanced minimal realization of a stable rational transfer function matrix. The Allison-Young algorithm for the interpolation problems is directly extended to matrix value cases and is applied in the realization procedure. This method uses the finite matrix of a Sarason operator instead of the infinite block Hankel matrix and the coefficients of the transfer function matrix instead of any initial realization. The advantage of this approach in connection with the solution of L^∞-optimization problems and the balanced realization is also discussed.