Evaluating and Approximating FIR Filters: An Approach Based on Functions of Matrices

Abstract

Most of the controllers designed for systems with timedelays involve finite impulse response (FIR) filters in their structure, in particular prediction based controllers for systems with input/output delays. We present theory, algorithms and software to evaluate the frequency response, to approximate the filters by stable linear timeinvariant systems and to compute their induced L-2 gain. The approach is based on the theory of functions of matrices. In the approach pole zero cancelations in frequency domain representations are explicitly taken into account.