Dissipativity and stability of a class of nonlinear multiple time delay integro-differential equations

This paper is concerned with the dissipativity and stability of the theoretical solutions of a class of nonlinear multiple time delay integro-differential equations. At the first, we give a generalized Halanay inequality which plays an important role in the study of dissipativity and stability of integro-differential equations. Then, we apply the generalized Halanay inequality to the dissipativity and the stability the theoretical solution of delay integro-differential equations (or by small ε perturbed) and some interesting results are obtained. Our results generalize a few previous known results. Finally, two examples are provided to demonstrated the effectiveness and advantage of the theoretical results.