Abstract

This paper deals with linear systems under sustained random perturbations. The stochastic perturbation model is given by a bounded Markov diffusion process, as it appears, e. g., in the description of load or generation uncertainties of power systems. For such systems, the Lyapunov exponents describe necessary and sufficient conditions for almost sure asymptotic stability. The present article reviews several numerical methods for the computation of Lyapunov exponents and applies this methodology to international test systems: four machines - ten bus and ten machines-thirty nine bus.