Robust H∞ control for LFC of discrete T–S fuzzy MAPS with DFIG and time-varying delays

The $H_{\infty }$ LFC control problem for a class of nonlinear power systems with time-varying delays is under study. Considering uncertainties arising from nonlinear issues such as the generation rate constraint (GRC) and governor dead band (GDB), as well as the high variability of renewable energy sources like wind power, the model is transformed into a discrete-time Takagi–Sugeno (T–S) fuzzy model with parameter uncertainty. By constructing a Lyapunov–Krasovskii functional, and employing difference inequalities and generalized cross-convex matrix inequalities, sufficient conditions for the asymptotic stability of power systems are provided. Based on the obtained conditions, a controller is designed to ensure the asymptotic stability of Multi-Area Power Systems (MAPS), with the performance index being $H_{\infty }$. Finally, simulation results demonstrate the correctness and effectiveness of the theorem.