ℌ∞ control for singular stochastic systems

In this paper, we deal with the bounded real lemma for stochastic singular systems with multiplicative noises. Based on the adaptation of Itô calculus, the admissibility for this class of systems is defined and the bounded real lemma is derived using the mean square exponential stability. This lemma is then used to synthetize a ℌ_∞ output feedback controller for the considered class of systems that achieves a given level of disturbance attenuation. The design is based on the solution of linear matrix inequalities coupled with an algebraic constraint.