Continuous Dependence on the Impulsive Effects of Dying Solutions of Systems Differential Equations with Variable Structure and Impulses

Abstract

Basic object of research in this paper are systems differential equations with variable structure and impulses. Switching moments, in which a change of the structure and impulsive effects on the solutions are determined by means of the switching hyperplanes, belonging to the phase space system. Changing the structure and impulsive effects on the solutions is performed at the switching moments, which are determined by the switching hyperplanes of phase space system.

The switching moments coincide with the moments, when the trajectory of corresponding initial problem meets the switching hyperplanes.

The main aim of this studies is ï¬nding the sufï¬cient conditions for continuous dependence of the solutions of systems differential equations, speciï¬ed above. We will clarify that:
- The solutions are dying due to the impulsive effects;
- Continuous dependence is on the perturbations in initial conditions and impulsive effects;
- Continuous dependence is on an arbitrary closed interval, which is contained in maximum interval of existence of the solutions.