Computation of the Frequency Response of Systems with Uncertain Parameters: A Simplification

Abstract

Computation of all possible frequency responses of a linear system that depends on M uncertain parameters is the subject of this paper. Using a brute force approach, this computation requires an M+1-dimensional parameter sweep, i.e. there is the usual frequency sweep plus one sweep for each uncertain parameter. If the system's transfer function has a linear dependence on the parameters, then determination of the frequency response can be greatly simplified. It has previously been shown that, for a single fixed frequency, all possible responses can be determined using several 1-dimensional sweeps. Thus, for a range of frequencies, the obvious extension would involve several 2-dimensional sweeps. However, this obvious extension is not the simplest way to carry out the computation. Indeed, this paper will show that all possible responses for a range of frequencies can be determined using just a finite number of 1-dimensional sweeps. This result is applicable to both continuous-time and discrete-time systems.