Output feedback guaranteed cost control for stochastic uncertain systems with multiplicative noise

The paper is concerned with the existence of a guaranteed cost controller for an uncertain system which is subject to structured uncertainty. The uncertainty in the system is assumed to have a stochastic character and satisfy certain stochastic integral quadratic constraints. It is shown that a guaranteed cost output feedback controller for a stochastic system can be synthesized as an output feedback controller absolutely stabilizing this system. For each initial state of the system, this controller can be found by parametric optimization of solutions of a pair of parameter-dependent generalized matrix Riccati inequalities or matrix Riccati equations arising in stochastic H_∞ theory