Asymptotic Stability of Nonzero Solutions of Discontinuous Systems of Impulsive Differential Equations

Abstract

Discontinuous systems of nonlinear non-autonomous differential equations with impulsive effects are the main object of investigation in the paper. These systems consist of two basic parts: (i) A set of non-linear nonautonomous systems of ordinary differential equations that define the continuous parts of the solutions. The right-hand sides of the systems are elements of the set of functions f = { f1, f2, ...} ; (ii) The conditions which consistently determine “the switching moments”. The structural change (discontinuity) of the right-hand side and impulsive perturbations take place at the moments of switching. In these moments, the trajectory meets the “switching sets”. They are parts of the hyperplanes, situated in the phase space of the system considered. Sufficient conditions are found so that the nonzero solutions of the studied discontinuous system with impulsive effects are asymptotically stable.