Modelling ellipsoidal uncertainty by multidimensional fuzzy sets

The paper addresses the problem of an aggregation of knowledge obtained from many sets of experiments each with different confidence level during identification of a linear dynamical system with uncertain parameters. The proposed approach describes the parameter space by a multidimensional fuzzy set specified by non-symmetric ellipsoidal α-cuts. An algorithm for determination of minimum confidence level guaranteeing stability of such a system is presented.

► We determine stability margin of a linear system with uncertain parameters.
► The uncertain parameters are modelled by a multidimensional fuzzy set.
► A knowledge obtained from many sets of experiments can be aggregated.
► A frequency domain approach is used to derive a computationally simple result.