Stability of linear stochastic systems via Lyapunov exponents and applications to power systems

This paper studies 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 paper presents several numerical methods for the computation of Lyapunov exponents and applies this methodology to linear oscillators in dimension 2 and 3, and to a one machine – infinite bus electric power system.