Stability analysis of delayed T-S fuzzy power system via a cubic function negative determination lemma

In this paper, a cubic function negative determination lemma is proposed for stability analysis of delay-dependent power systems with energy storage systems (ESSs). Firstly, a Takagi-Sugeno (T-S) fuzzy power system model with ESS is constructed by analyzing the nonlinear characteristics caused by the valve position restriction. Secondly, a fuzzy proportional-integral (P-I) controller is adopted to stabilize this fuzzy power system. Then, a negative determination lemma for cubic functions is developed to determine the allowable delay upper bound (ADUB) for the delayed fuzzy power system. Using the proposed lemma as well as the Lyapunov-Krasovskii functional (LKF), stability criteria are derived. In addition, a binary search algorithm is employed in order to reduce the computational burden when obtaining the ADUB. Finally, the effectiveness of the proposed methods is verified by two case studies.