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

Abstract

This paper addresses a mode-dependent state-feedback H∞ control for descriptor hybrid systems, considering both the absence and presence of actuator saturation. Firstly, the necessary and sufficient conditions for the stochastic admissibility criterion with H∞ performance ? of the closed-loop system is 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 given state-feedback control input and a virtual control input that 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 LMI conditions for the existence of the mode-dependent state-feedback H∞ control and the ellipsoidal shape of invariant set are successfully derived. Two numerical examples demonstrate the effectiveness of the proposed approach in optimizing H∞ performance $\gamma$ and identifying the largest invariant set.