Stability Robustness Bounds for State-Space Models with Dependent Uncertainty: Application to a Microgrid System

Abstract: In this paper stability robustness bounds for linear state space models with dependent uncertainty based on the Lyapunov stability method and time-invariant perturbation method are applied to a microgrid system. In contrast to previous observations, it is shown that the Lyapunov stability bound gives better result than the time-invariant perturbation bound for a dependent uncertainty for the open-loop microgrid system. It is also shown that the Lyapunov stability bound gives larger value for the closed-loop microgrid system with the linear quadratic regulator control.

Keywords: Robust Control, Microgrid, Lyapunov Method, Stability, State-Space Model, Dependent Uncertainty.