Applications of a Lyapunov function with a homogeneous derivative

The application of a Lyapunov function with a homogeneous derivative to investigate the stability of dynamic systems is presented. The problem of the region of attraction for nonlinear autonomous stable systems is investigated by this approach, and an estimation of the region of attraction is given. The stable equilibrium point concerned may be non-hyperbolic. The method is also extended to time-varying nonlinear systems and some sufficient conditions for these to be asymptotically stable are obtained.