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.