Novel Performance of T-S Fuzzy Power System Based on a New Slack Lemma and an Optimization Algorithm

This paper studies performance analysis and load frequency control (LFC) for a Takagi–Sugeno (T-S) fuzzy power system equipped with an energy storage unit. A corresponding T-S fuzzy representation of the system is constructed. Subsequently, a new lemma of slack Lyapunov function is constructed, which relaxes the conventional positive-definiteness requirement on the quadratic form, provides additional flexibility in the LMI formulation, and yields less conservative stability conditions. In addition, a genetic-algorithm-based outer search is employed to optimize the scalar parameter ϱ, while the associated LMIs are solved using the LMI solver, thereby reducing the conservatism of the stability conditions and enlarging the maximum allowable delay bound. Simulation cases are finally presented to confirm the feasibility and effectiveness of the proposed methods. The proposed method increases the maximum allowable delay bound by 2.6920%, 4.0220% and 4.0528% compared with the reference method for the tested controller parameters.