Analysis of linear systems with fuzzy parametric uncertainty

Abstract

In this paper the problem of determining the stability margin of a linear system with fuzzy parametric uncertainty is addressed. This kind of systems arise when the exact value of a process parameter is not available, but an estimation of the value is given by an expert (“more or less 5”). As the α-cut representation of a fuzzy number is a functional interval, interval analysis shows to be a suitable tool to deal with fuzziness. Based on the Argoun's stability test for interval systems, a new methodology, with a natural graphical interpretation, is presented. An independent confidence degree for every coefficient is considered, allowing a clear understanding on how each coefficient affects stability. An analysis on how precise one should be on some coefficients to allow more uncertainty on others can be carried out. A comparison with Tsypkin–Polyak plot is also presented.