STABILITY RADII OF SYSTEMS WITH STOCHASTIC UNCERTAINTY AND THEIR OPTIMIZATION BY OUTPUT-FEEDBACK

We consider linear plants controlled by dynamic output feedback which are subjected to blockdiagonal stochastic parameter perturbations. The stability radii of these systems are characterized, and it is shown t hat, for real data, the real and the complex stability radii coincide. A corresponding result does not hold in the deterministic case, even for perturbations of single-output feedback type. Ln a second part of the paper we study the problem of optimizing the stability radius by d ynamic linear output feedback. Necessary and sufficient conditions are derived for the existence of a compensator which achieves a suboptima l stability radius. These conditions consist of a parametrized Riccati equation, a parametrized Liapunov inequality, a coupling inequality, and a number of linear matrix inequalities (one for each disturbance t erm). The corresponding problem in the deterministic case, the optimal mu-synthesis problem, is still unsolved.