Optimal Hankel-norm model reductions: Multivariable systems

This paper represents a first attempt to derive a closed-form (Hankel-norm) optimal solution for multivariable system reduction problems. The basic idea is to extend the scalar case approach in [5] to deal with the multivariable systems. The major contribution lies in the development of a minimal-degree-approximation theorem and an efficient computation algorithm. The main theorem describes a closed-form formulation for the optimal approximants, with the optimality verified by a complete error analysis. Many useful singular value and vector properties associated with block Hankel matrices are also explored. The main algorithm consists of three steps: (i) compute the right matrix-fractiondescription of an adjoint system matrix, (ii) solve a (algebraic) Riccati-type equation, and (iii) find the partial fraction expansion of a rational matrix.