Set invariance analysis for Lipschitz continuous singular systems subject to actuator saturation

In this paper, the set invariance problem for Lipschitz nonlinear continuous singular systems with actuator saturation is considered. A saturation allowance feedback approach is adopted to deal with actuator saturation. A sufficient condition for the existence of state feedback controller is proposed. It can guarantee the existence and uniqueness of solution and contractive invariance of the closed-loop system with respect to a given ellipsoid simultaneously. The estimation of largest contractively invariant ellipsoid is formulated to an optimization problem with linear matrix inequality (LMI) constraints. Moreover, the method is extended to solve the robust fault tolerant control problem for nonlinear singular systems with both actuator saturation and failures. Finally, a numerical example is provided to illustrate the effectiveness and less conservativeness of the proposed approach.