Approximation of discrete linear systems

Abstract

Given a multi–input, multi–output linear time–invariant discrete–time system or its weighting matrices, equations are derived to characterize a system of lower dimension which optimally approximates the given system with respect to the sum of squared output errors of the impulse response. These equations are shown to imply that in principle a modified B. L. Ho algorithm can be used to find the approximation. The connection with projection methods of approximation is demonstrated, Some comments on computational difficulties are included.