REDUCTION THEOREMS IN THE PROBLEM OF STABILITY OF THE CRITICAL EQUILIBRIA OF IMPULSIVE DIFFERENTIAL EQUATIONS

摘要

We substantiate the reduction principle for a class of systems of impulsive differential equations (impulsive systems). This class is characterized by the property that the matrices of linear approximation of the impulsive system are commutative. We reduce the problem of stability of an equilibrium state of the impulsive system in the critical case to the problem of existence of a Lyapunov function for some auxiliary (model) impulsive system. The model system contains solely the critical variables.