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 = f(t, x), t not equal theta(i)(x) Delta x\t = theta(i)(x) = J(i)(x), i is an element of N = {1,2...}, where Delta x\(t=theta) := x(theta +) - x(theta), x(theta +) = lim(t -->theta) +x(t). The Lyapunov second method is used as a tool in obtaining the criteria for stability, asymptotic stability, and instability of the trivial solution. (C) 2000 Academic Press.