Invariance principles for delay differential inclusions

This paper establishes two invariance principles for delay differential inclusions. The delay differential inclusions are required to satisfy the basic assumptions: the right-hand sides are upper semicontinuous and take nonempty compact and convex values on the domains. The classical LaSalle's invariance principle for delay differential inclusions is established successfully by locally Lipschitz Lyapunov-Krasovskii functionals and several stability corollaries are developed. Besides, the concept of limit delay differential inclusions is proposed to generalize the invariance principle to time-varying delay differential inclusions. Some numerical examples are given to show the effectiveness of the proposed results.