Randomized algorithms for probabilistic robustness with real and complex structured uncertainty

In recent Sears, there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems, Unli ke classical worst case methods, these algorithms provide probabilistic est imates assessing, for instance, if a certain design specification is met wi th a given probability. One of the advantages of this approach is that the robustness margins can be often increased by a considerable amount, at the expense of a small risk. In this sense, randomized algorithms may be used b y the control engineer together with standard worst case methods to obtain additional useful information, The applicability of these probabilistic methods to robust control is prese ntly limited by the fact that the sample generation is feasible only in ver y special cases which include systems affected by real parametric uncertain ty bounded in rectangles or spheres, Sampling in more general uncertainty s ets is generally performed through overbounding, at the expense of an expon ential rejection rate. In this paper, randomized algorithms for stability and performance of linea r time invariant uncertain systems described by a general M-Delta configura tion are studied, In particular, efficient polynomial-time algorithms for u ncertainty structures Delta consisting of an arbitrary number of full compl ex blocks and uncertain parameters are developed.