Security Sampled-Data-Based $H_{\infty }$ Control for Interval Type-2 Fuzzy Systems via SML Algorithm and Its Applications

This article focuses on the issues of security sampled-data-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control design for interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems against false-data injection (FDI) attacks and external disturbances using a supervision of machine learning (SML) algorithm. To improve the bounds of sampled data period, an SML algorithm is proposed to optimize the allocation of network resources and ensure the effective utilization of bandwidth. Besides, two improved integral inequalities are introduced to estimate the integral quadratic terms that account for signal transmission delays and sampling information. Meanwhile, an appropriate asymmetric looped Lyapunov-Krasovskii functional (ALLKF) is constructed incorporating information on the fuzzy membership function (FMF), aperiodic sampling pattern, and transmission delays to facilitate model conservativeness. Next, based on the constructed fuzzy ALLKF along with the proposed inequalities, a set of necessary conditions for achieving asymptotic stability with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance is derived through linear matrix inequalities (LMIs), and then control parameters can be obtained to guarantee the less conservative stabilization results of considered closed-loop systems. Finally, to verify the superiority and feasibility of the proposed theoretical observations, the hacked permanent magnet synchronous generator (PMSG)-based wind energy system (WES) is numerically validated. Additionally, comparative examples are presented to demonstrate the improved conservativeness of the proposed technique.