Fault detection filter design for interval type-2 fuzzy systems under a novel adaptive event-triggering mechanism

This study is concerned with the problem of event-based fault detection (FD) filter design for interval type-2 fuzzy systems in a network environment. Firstly, by employing the properties of exponential function, a novel adaptive event-triggering mechanism (AETM) where the boundedness of threshold function is guaranteed and the size of threshold function is inversely proportional to the size of 2-norm of the sampled-output-error is proposed to dynamically adapt the variation of the system and to reduce the unnecessary information communication between the sensor and the filter. Secondly, in the framework of time-delay systems, the FD system with a networked filter and an AETM is modelled as an interval time-varying delayed system. Then, a sufficient condition to implement co-design of the parameters of filter and trigger is obtained by applying a simple Lyapunov–Krasovskii functionals, combined with recently developed Wirtinger-based integral inequality and reciprocally convex inequality, and utilising congruent transformation method. Thirdly, based on the obtained co-design condition, an optimisation algorithm subject to convex constraints for the tradeoffs between resource utilisation and $H_\infty $H∞ performance of the FD system is further developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed scheme.