Minimal state space realization for transfer functions represented by coefficients using generalized orthonormal basis

Given the expansion coefficients γ_l^k of a rational transfer function G in a generalized orthonormal basis generated by an inner function m, one can construct a state space representation starting from the balanced realization of m, but that representation is not minimal-even in the SISO case-in general. Therefore one needs an algorithm to construct a minimal representation. This paper gives a generalization of the celebrated Ho-Kalman algorithm that provides the desired minimal representation