Investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces

Abstract In this work sufficiently conditions, boundedness, stability, asymptotical stability, exponential stability, attraction, practical stability, nondisturbed motion systems with impulse perturbations on some hypersurfaces are obtained. We formulate the conditions which guarantee that no beating motion of hypersurfaces will be present. Estimates of Cauchy matrix system of variation for approximated system are obtained for different kinds of right side shorted system. These estimates are used as one-parametric scale increasing functions; moreover we also consider two-parametric scale, such as proposed by Demidovich.