Stability of differential equations with piecewise constant arguments of generalized type

AKHMET M.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.68, no.4, pp.794-803, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.1016/j.na.2006.11.037
  • Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.794-803
  • Keywords: stability, quasilinear systems, piecewise constant argument of generalized type, PERIODIC-SOLUTIONS, DELAYS
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper we continue to consider differential equations with piecewise constant argument of generalized type (EPCAG) [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA 66 (2007) 367-383]. A deviating function of a new form is introduced. The linear and quasilinear systems are under discussion. The structure of the sets of solutions is specified. Necessary and Sufficient conditions for stability of the zero Solution are obtained. Our approach can be fruitfully applied to the investigation of stability, oscillations, controllability and many other problems of EPCAG. Some of the results were announced at The International Conference on Hybrid Systems and Applications, University of Louisiana, Lafayette, 2006. (c) 2006 Elsevier Ltd. All rights reserved.