Stability of differential equations with piecewise constant arguments of generalized type


AKHMET M.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, cilt.68, ss.794-803, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 68 Konu: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/j.na.2006.11.037
  • Dergi Adı: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Sayfa Sayıları: ss.794-803

Özet

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.