FIR approximation of linear systems from quantized records

Abstract

In this paper we consider the problem of identifying a fixed-order FIR approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization. In particular, a FIR model of given order which provides the best approximation of the input-output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. First we show that the considered problem can be formulated in terms of robust optimization. Then, we present two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques. The effectiveness of the proposed approach is illustrated by means of a simulation example.