Method of Lyapunov functions for differential equations with piecewise constant delay


AKHMET M., Arugaslan D. , YILMAZ E. O.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.235, no.16, pp.4554-4560, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 235 Issue: 16
  • Publication Date: 2011
  • Doi Number: 10.1016/j.cam.2010.02.043
  • Title of Journal : JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Page Numbers: pp.4554-4560

Abstract

We address differential equations with piecewise constant argument of generalized type [5-8] and investigate their stability with the second Lyapunov method. Despite the fact that these equations include delay, stability conditions are merely given in terms of Lyapunov functions; that is, no functionals are used. Several examples, one of which considers the logistic equation, are discussed to illustrate the development of the theory. Some of the results were announced at the 14th International Congress on Computational and Applied Mathematics (ICCAM2009), Antalya, Turkey, in 2009. (C) 2010 Elsevier B.V. All rights reserved.