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

Abstract

ABSTRACTThis 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 performance of the FD system is further developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed scheme.