Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay

Stabilization and disturbances rejection for nonlinear differential inclusions with time-delay are devoted in this paper. The Lyapunov-Krasovskii functional is constructed with the help of the convex hull Lyapunov function, and the convex hull Lyapunov function is obtained by solving linear matrix inequalities using MATLAB software. Sufficient conditions for stabilization are acquired and a continuous state feedback law is designed such that the closed-loop system is asymptotically stable. The method can be applied to stabilize a class of uncertain systems with time-delay. Further, disturbances rejection with minimal reachable set is studied under two types of disturbances. Finally, two examples are given to illustrate the effectiveness of the proposed design technique.