Stability analysis of linear time-delay differential inclusion systems subject to input saturation

Stability analysis of linear differential inclusion systems with time-delay and input saturation is devoted in this study. The convex hull Lyapunov function is used to construct Lyapunov-Krasovskii functionals. A continuous state feedback law is designed. By the state feedbacks, sufficient conditions for saturated stabilisation are acquired and the domain of attraction is estimated. Furthermore, disturbance rejection with minimal reachable set is studied under two types of disturbances. Moreover, least L₂ gain is obtained under the unit energy disturbances. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design technique.