Retracted: State estimation of Takagi-Sugeno fuzzy system in networked control system with stochastic time delays under unknown attacks

This article concerns the event-triggered fuzzy filter design for Takagi-Sugeno (T-S) fuzzy systems subject to deception attacks under the stochastic multiple time-varying delays. A sequence of random variables, which are mutually independent but obey the Bernoulli distribution, is introduced to account for the randomly occurring communication delays. In order to efficiently utilize limited network communication bandwidth resources, the event-triggering scheme is adopted. A fuzzy filter with the attacked input signal is presented. Moreover, due to communication delays caused by event-triggering schemes and transmission, the filter adopts non-synchronous premise variables with the system. Then, by utilizing a model transformation technique, the fuzzy systems are developed. Furthermore, using the piecewise Lyapunov functional method technique, the resulting criterion provides sufficient conditions to ensure that fuzzy systems under deception attacks are stochastically stable with an H_∞ performance. Accordingly, the conditions for the co-design of the fuzzy filter and event-triggering schemes are given. Finally, numerical simulation with the industrial process provided to verify the proposed event-triggered design.