Generalized Halanay inequalities for dissipativity of Volterra functional differential equations

This paper is concerned with the dissipativity of theoretical solutions to nonlinear Volterra functional differential equations (VFDEs). At first, we give some generalizations of Halanay's inequality which play an important role in study of dissipativity and stability of differential equations. Then, by applying the generalization of Halanay's inequality, the dissipativity results of VFDEs are obtained, which provides unified theoretical foundation for the dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay-integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice. (C) 2008 Elsevier Inc. All rights reserved.