The critical perturbation radius weights in H∞ synthesis for interval plants

In this paper the H_∞ synthesis of robust controllers for interval plants is considered. Generally, the uncertainties which the H_∞ method deals with are modeled as nonparametric (norm-bounded) uncertainties, and a weighting function is used to specify the frequency-selective effects of the uncertainties. The first attempt to deal with the synthesis problem for a SISO interval plant using H_∞ methods, used the maximum perturbation radius (MPR) as the weight. Unfortunately, the MPR which only yields a sufficient stability condition, not only introduces conservatism but also becomes computationally inefficient for general interval perturbations. The more recently introduced critical perturbation radius (CPR) yields necessary and sufficient conditions for robust stability and is thus an ideal candidate for a systematic methodology in defining nonconservative H_∞ uncertainty weights. This paper illustrates the application of the CPR weights and shows that significant improvements can be obtained using the critical perturbation radius rather than maximum perturbation radius