Algorithms and software for approximating and evaluating FIR filters

The controllers designed for time-delays systems often involve finite impulse response (FIR) filters, in particular prediction based controllers for systems with input/output delays. We present algorithms and software to evaluate the frequency response, to approximate the filters by stable linear time-invariant systems and to compute their induced L2 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.