Stability in cellular neural networks with a piecewise constant argument


AKHMET M., ARUĞASLAN ÇİNÇİN D., YILMAZ E.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.233, no.9, pp.2365-2373, 2010 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 233 Issue: 9
  • Publication Date: 2010
  • Doi Number: 10.1016/j.cam.2009.10.021
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.2365-2373
  • Keywords: Cellular neural networks, Differential equations with a piecewise constant argument of generalized type, Lyapunov-Razumikhin technique, Method of Lyapunov functions, Linear matrix inequality, GLOBAL ASYMPTOTIC STABILITY, DIFFERENTIAL-EQUATIONS, EXPONENTIAL STABILITY, CONTINUOUS-TIME

Abstract

In this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1-4], a model of cellular neural networks (CNNs) [5,6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results. (C) 2009 Elsevier B.V. All rights reserved.