Minimal Realization and Irreducible Transfer Function Matrix with Minimum Number of Parameters

Abstract

On the minimal realization from the Markov parameters of a linear dynamical system, beautiful results were obtained by Ho-Kalman and Rissanen. In particular, the Rissanen algorithm is superior in generality, simplicity, recursive structure, and numerical stability. However, it has redundancy. For example, it produces n(n+3)/2 parameters for a strictly proper linear scalar system, while the transfer function of that system has at most 2n parameters.
In this paper, an algorithm for the minimal realization from the Markov parameters of linear constant multivariable system is obtained which produces an observable (controllable) canonical form realization with minimum number of parameters and preserves the superior properties in the Rissanen algorithm. Further, from this algorithm the irreducible matrix fraction description with minimum number of parameters is easily derived.