Integro-sum inequalities and motion stability of systems with impulse perturbations

Abstract This article is devoted to the investigation of the properties of motion represented by essential nonlinear system of differential equations with impulse effect. The results, based on the solvability problem by S.A. Chaplygin for discontinuous functions, satisfy “integro-sum” inequalities. The conditions of boundedness, stability, asymptotical stability, practical stability, attraction motion for different kinds of nonlinearities of systems are obtained.