Generalized Halanay inequality and its application to delay differential inclusions

In this work, by using a generalized Halanay inequality, a regular Lyapunov function and the theory of nonsmooth analysis, we investigate the uniformly ultimate boundedness of the zero solution for nonautonomous delay differential inclusions. The sufficient condition is presented in integral form, which is different from the ones given in some related literature. We also provide different characterizations of the sufficient conditions on the stability, the asymptotic stability, and the exponential stability of the zero solution for nonautonomous delay differential inclusions. Finally, one example is given to illustrate the effectiveness of the theoretical results obtained. (c) 2024 Elsevier Ltd. All rights reserved.