Estimate of the attraction domain for a class of nonlinear switched systems

We consider a hybrid dynamical system composed of a family of subsystems of nonlinear differential equations and a switching law which determines the order of their operation. It is supposed that the subsystems are homogeneous with homogeneity degrees less than one, and the zero solutions of all the subsystems are asymptotically stable. Based on the Lyapunov direct method and the differential inequalities method, we derermine classes of switching laws providing prescribed estimates of attraction domains for the zero solutions of the corresponding hybrid systems. The developed approaches are used for the stabilization of a double integrator.