On the probabilistic characterization of model uncertainty and robustness

Abstract

This paper considers the probabilistic characterization of model uncertainties and stability robustness on the Nyquist diagram. For any given /spl epsi/>0, any frequency /spl omega/, we describe the boundary of a domain D/sub /spl epsi/,/spl omega// such that the frequency response of an uncertain plant at that frequency /spl omega/ is guaranteed in the domain with a probability of at least 1-/spl epsiv/ where /spl epsiv//spl les//spl epsi/ is a function of /spl epsi/ and frequency /spl omega/ and a upper bound of /spl epsiv/ can be estimated easily. Then, by analyzing the evolution of the boundary of D/sub /spl epsi/,/spl omega// as a function of the frequency /spl omega/, a combined curve C is constructed such that it includes the boundary of a domain D/sub /spl epsi// covering the Nyquist plot with a probability of at least 1-/spl epsiv/ for a range of frequencies.