Generalized Halanay inequalities for dissipativity of Volterra functional differential equations

• Published in: Journal of mathematical analysis and applications Vol. 347; no. 1; pp. 169 - 178
• Main Authors: Wen, Liping, Yu, Yuexin, Wang, Wansheng
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.11.2008; Elsevier
• Subjects: Difference and functional equations, recurrence relations; Dissipativity; Dynamical systems; Exact sciences and technology; Finite differences and functional equations; Halanay's inequality; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; Volterra functional differential equations; Volterra functional differential equations; Halanay's inequality; Dissipativity; Dynamical systems; Differential equation; Functional equation; Delay equation; Functional; Mathematical analysis; Volterra functional differential equations;Dynamical systems;Dissipativity;Halanay's inequality; Halanay inequality; System analysis; Application; Integrodifferential equation; Volterra equation; Volterra integral equations; Numerical stability
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2008.05.007

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.