Fault Detection for Fuzzy Systems With Multiplicative Noises Under Periodic Communication Protocols

This paper is concerned with the fault detection problem for a class of networked fuzzy systems with multiplicative noises on both system states and measurement outputs. In view of the limited communication capacity, a periodical communication protocol (i.e., the round-robin protocol) is adopted to undertake the transmission task between the sensors and the fault detection filter, which leads to periodical delays in the overall system. A Takagi–Sugeno fuzzy-model-based fault detection filter is constructed to produce the residual signal and an auxiliary error system is established to facilitate the stability analysis of the error dynamics. With the aid of Lyapunov stability theory, sufficient conditions are obtained that ensure the exponentially mean-square stability of the error dynamics with prescribed $H_{\infty }$ performance constraint. The desired fault detection filter is designed by solving a convex optimization problem via the semidefinite programme method. A finite-time evaluation function and an adjustable threshold are introduced in order to detect the possible faults effectively. The effectiveness of the proposed fault detection scheme is validated by a numerical simulation example.