Probability-guaranteed robust H_∞ performance analysis

This paper addresses the common engineering practice of specifying a required probability of attaining some performance level. The problem setup is that of a standard robust H_∞ performance analysis of a parameter-dependent system, except that the parameter hyper-rectangle (box) shrinks in the analysis in order to accommodate a polytopic performance goal that is better than the one attainable for the original parameter box. An affine-quadratic, multiconvex approach is applied to reduce the overdesign that is inherent in the quadratic approach. A version of the Bounded Real Lemma (BRL) in the form of BiLinear Matrix Inequalities (BLMIs) guarantees a minimum H_∞-norm for a prescribed probability. These BLMIs are solved using an iterative algorithm. A uniform distribution is assumed for the system parameters, according to the uniformity principle. The probability requirement is expressed by a set of LMIs that is derived by extending an existing second-order cone method; these LMIs are to be concurrently solved with the BRL BLMIs. The proposed analysis is demonstrated via a 2-parameter example.