On the general problem of stability for impulsive differential equations

Criteria for stability, asymptotical stability and instability of the nontrivial solutions of the impulsive system dx/dt = f (t, x), t not equal theta(i) (x), Deltax\(t =thetai) (x) = I-i(x), i is an element of N = {1, 2,...}, where Deltax\(t=theta) := x (theta+) -x(theta), x(theta+) = lim(t-->inverted iotatheta) + x(t) are obtained by Lyapunov's second method. The construction of a reduced system in the neighbourbood of a nontrivial solution is a central auxiliary result of the paper. (C) 2003 Elsevier Inc. All rights reserved.