Stabilization of nonlinear PMSG-based wind energy conversion system via coupling memory sampled-data control with a membership function-dependent $ H_{\infty} $-approach

Abstract This study presents the coupling memory sampled-data control (CMSDC) design for the Takagi-Sugeno (T-S) fuzzy system that solves the stabilization issue of a surface-mounted permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS). A fuzzy CMSDC scheme that includes the sampled-data control (SDC) and memory sampled-data control (MSDC) is designed by employing a Bernoulli distribution order. Meanwhile, the membership function-dependent (MFD) H∞ performance index is presented, mitigating the continuous-time fuzzy system's disturbances. Then, by using Lyapunov-Krasovski functional with MFD $H_\infty$ performance index, data of sampling pattern and a constant signal transmission delay, sufficient conditions are derived. These sufficient conditions are linear matrix inequalities (LMIs), ensuring the global asymptotic stability of PMSG-based WECS under the designed control technique. Besides, the proposed method is demonstrated by a numerical simulation implemented on the PMSG-based WECS. Finally, Rossler's system demonstrates the effectiveness and superiority of the proposed method.