Robust stochastic stability of power system with time-varying delay under Gaussian random perturbations

In this paper, by taking into account the stochastic perturbations, the power system with time-varying delay under Gaussian random perturbations is formulated into the stochastic differential equation, then the robust stochastic stability is discussed in detail. Based on Lyapunov stability theory, some improved robust stability and robust stochastic stability criteria are developed, where the restrictions on the derivative of time-varying delay are removed so as to reduce the conservatism. The obtained results formulated in the form of linear matrix inequalities (LMIs) can be effectively solved by the LMI toolbox. Finally, one machine and infinite system under random perturbations is provided to demonstrate the effectiveness and usefulness of the developed results.