  In this paper, a new polynomial chaos based framework for analyzing linear
systems with probabilistic parameters is presented. Stability analysis and
synthesis of optimal quadratically stabilizing controllers for such systems are
presented as convex optimization problems, with exponential mean square
stability guarantees. A Monte-Carlo approach for analysis and synthesis is also
presented, which is used to benchmark the polynomial chaos based approach. The
computational advantage of the polynomial chaos approach is shown with an
example based on the design of an optimal EMS-stabilizing controller, for an
F-16 aircraft model.
