Continuous Dependence on the Initial Condition of the Solution of a System of Differential Equations with Variable Structure and with Impulses

Abstract

In the paper an initial value problem is considered for a system of ordinary differential equations with variable structure and impulses. Sufficient conditions are found under which there exists a solution of such system for $t\ge {\tau }_0$ where ${\tau }_0$ is a real constant. Sufficient conditions are presented for continuous dependence of the solution of the initial condition.