Stability of the Zero Solution of Impulsive Differential Equations by the Lyapunov Second Method

The paper is concerned with the stability of the zero solution of the impulsive system dx dt sf t, x., t/ui x. D x < tsu i x .sJi x., igNs 1, 2, . . .4, where D x < tsu[x uq.yx u., x uq.slim tªuqx t.. The Lyapunov second method is used as a tool in obtaining the criteria for stability, asymptotic stability, and instability of the trivial solution.