Synthesis of ℋ_∞ Control for Descriptor Hybrid Systems with Actuator Saturation

This paper addresses a mode-dependent state-feedback (Formula presented.) control for stochastic descriptor hybrid systems, considering both the absence and presence of actuator saturation. Firstly, the necessary and sufficient conditions for the stochastic admissibility criterion with (Formula presented.) performance (Formula presented.) of the closed-loop system are proposed. Given the proposed non-convex condition, the author reformulates it into linear matrix inequalities (LMIs). Then, to extend the result to the systems with actuator saturation, the actuator-saturated control input is expressed as a linear combination of a given state-feedback control input and a virtual control input that always remains under the saturation level. To verify this expression, the set invariant condition is also suggested by using the singular mode-dependent Lyapunov function candidate. Therefore, the conditions for the existence of both the mode-dependent state-feedback (Formula presented.) control and the ellipsoidal shape invariant sets are successfully derived in terms of LMIs. Two numerical examples demonstrate the effectiveness of the proposed method by solving optimization problems subject to the proposed LMIs that minimize (Formula presented.) performance (Formula presented.) and maximize the invariant set, respectively.