On the existence of a lyapunov function as a quadratic form for impulsive systems of linear differential equations

Abstract

A. O. Ignat'ev UDC 517.925 A system of linear differential equations with pulse action at fixed times is considered. We obtain sufficient conditions for the existence of a positive-definite quadratic form whose derivative along the solutions of differential equations and whose variation at the points of pulse action are negative-definite quadratic forms regardless of the times of pulse action.