Set invariance analysis for Lipschitz discrete-time singular systems with actuator saturation

This paper considers the set invariance problem for Lipschitz nonlinear discrete-time singular systems subjected to actuator saturation. Firstly, by using fixed point principle, a sufficient condition of the existence and uniqueness of a solution for the closed-loop system is obtained. Then based on saturation allowance feedback approach, a sufficient condition such that the closed-loop system is regular, causal and set contractively invariant is established. Finally, the state feedback gain design method and invariant ellipsoid estimation algorithm are proposed.