| Abstract: | ![]()
A new approach of the Lyapunov type is presented for the stability analysis of a class of time invariant, nonlinear dynamical systems, which are characterized by a periodic nonlinearity, and the existence of an infinite number of stationary states. In particular, the method can be applied for studying transient stability problems in power systems, and the synchronization of phase lock circuits. Frequency criteria are developed for the convergence of all solutions to an equilibrium state, and a procedure, based on these criteria, is outlined for constructing stability regions for a collection of neighboring equilibria. When applied to power—or phase lock systems, these regions can be interpreted as synchronization regions within an arbitrary, given number of cycles. Also, some new results are obtained with respect to synchronization conditions within the first cycle. |
