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 could be carried out using an (m + l)-dimensional parameter sweep, i.e. there is the usual frequency sweep plus one sweep for each uncertain parameter. A much simpler computational alternative is possible if the uncertain system's transfer function has a linear dependence on the parameters and if the set of possible parameter values has a polytopic structure. For this class of uncertain systems, 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.

Additional information

Notes on contributors

ANDREW C. BARTLETT

Now with the Electrical and Computer Engineering Department, University of Michigan-Dearborn, Dearborn, MI 48121, U.S.A.