Sampled‐data stabilization analysis of T‐S fuzzy PMSG‐based wind turbine system under gain fluctuations

This study is about the stabilization of fuzzy nonfragile retarded sampled‐data control (NRSDC) of a permanent magnet synchronous generator (PMSG)‐based wind turbine system (WTS) under randomly occurring control gain fluctuations. First, the considered nonlinear model is represented as an equivalent Takagi–Sugeno (T‐S) fuzzy linearized model through IF‐THEN rules. Next, an effective NRSDC with a specified time lag is presented which also accounts for the unpredictable controller gain fluctuations. To do this, the fluctuations in controller gains are randomly generated with the Bernoulli order distribution. Then, sufficient conditions are derived in the form of a solvable linear matrix inequality (LMI) expressed as a combination of the Lyapunov–Krasovskii function (LKF) and loop function (LPF) to ensure overall asymptotic stability. Also, disturbance attenuation is taken to ensure the control efficacy. Finally, the method proposed in this study is verified for its applicability through the simulation of nonlinear PMSG‐based WTS. In addition, Rossler's system is used to show its superiority and feasibility through comparison with some conventional methods.