Stability of Differential Systems with Impulsive Perturbations in Terms of Two Measures
The study of differential systems of the form (1.1) [see pdf for notation] where [see pdf for notation] denotes the distributional derivative of [see pdf for notation], a function of bounded variation (that is, differential systems with impulsive perturbations, also called measure differential equations), is both interesting and important because most models for biological neural nets,pulse frequency modulation systems, automatic control problems with impulsive inputs and many physical processes are best described by such equations [1-3,8,10,12,13]. Since the solutions of (1.1) are discontinuous (that is, functions of bounded variation), the investigation of the stability properties of (1.1) by the usual techniques of perturbation theory and differential inequalities offers many difficulties. However, in [3,8] some stability results have been obtained under certain assumptions which may be regarded restrictive. See also [1,10,13].