Absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty

This paper is concerned with existence and optimality properties of so-call ed guaranteed cost controllers for an uncertain system subject to structure d uncertainty. The uncertainty in the system is assumed to have a stochasti c character and to satisfy certain stochastic integral constraints. It is s hown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolu tely stabilizing this system. For each initial state of the system, this co ntroller can be found by parametric optimization of solutions of a paramete r-dependent generalized matrix Riccati equation arising in stochastic H-inf inity theory.