Robust stabilization of time-delayed electric vehicle aggregator via exponential Lyapunov Krasovskii functional

Abstract

The exponential stability of time-varying delayed linear systems under uncertainty is the subject of this paper. A low-conservative approach for stabilizing an electric vehicle (EV) aggregator is described with the use of a novel Lyapunov–Krasovskii Functional (LKF) with an exponential term. The present paper considers the state space model of the system as a polytopic model, and integrates this approach with free-weighting auxiliary matrices to yield an exact allowable delay upper bound (ADUB). The Lyapunov theory is used to prove system stability without any limitation on the maximum upper bound of delay derivative in the presence of a time-varying delay and uncertain participation factors. A load frequency control (LFC) system with EV aggregators is introduced to illustrate the performance of the proposed method. Various scenarios are conducted to illustrate the superiority of the proposed approach over previous methods. The results indicate that the proposed approach calculates a larger ADUB than the state-of-the-art techniques for both the nominal and uncertain power systems cases.