$H_{\infty }$ Fuzzy Fault Detection for Uncertain 2-D Systems Under Round-Robin Scheduling Protocol

This paper is concerned with the robust <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> fault detection problem for a class of uncertain discrete-time nonlinear 2-D systems subject to Round-Robin scheduling protocol. The Takagi–Sugeno fuzzy model is used to approximate the nonlinearities, where the linear fractional uncertainties enter the system in a random way. A kind of widely used communication mechanism, namely, Round-Robin communication protocol, is adopted to periodically schedule the sensors and the fault detectors to realize the information exchange in order to reduce the bandwidth usage in a networked environment with limit resource. An improved 2-D fuzzy residual generator is constructed to detect the possible fault, where the stability analysis of the resulting augmented 2-D system is discussed. It is accomplished by using a combination of the basis-dependent Lyapunov-like function and the stochastic analysis techniques. Sufficient conditions are first established to guarantee the globally asymptotic stability of the error dynamics of the state estimation with prescribed <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> performance constraints. Then, a residual generator is proposed to detect the possible faults. The effectiveness of the developed algorithm is demonstrated via application to the fault detection problem for a thermal process.