Matrix impulsive system of differential equations with bilinear main part

Abstract:
The main purpose of the paper is to summarize some fundamental results concerning the matrix impulsive differential equations with bilinear main part. The conditions of existence of solutions of homogeneous and nonhomogeneous impulsive matrix equation have been determined. The periodic solution of matrix impulsive equation has been considered. The condition of existence the unique periodic solution has been obtained. The invariant set of impulsive matrix equation has been studied. The condition of its existence for nonlinear matrix equation has been determined.