Stabilisation for one-sided Lipschitz non-linear differential inclusions

Stabilisation design methods for one-sided Lipschitz non-linear differential inclusions are considered in this study. Sufficient conditions of exponential stabilisation for the closed-loop system are given by solving linear matrix inequalities. Two kinds of continuous control laws are designed such that the closed-loop systems are exponentially stable at the origin, respectively. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design technique.