H_ /H∞ faults detection for discrete-time nonlinear complex dynamical networks with Markov jump topology

Abstract

The fault detection issue for discrete-time nonlinear complex dynamical networks (CDNs) with Markov jump topology is investigated. Firstly, an interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model is used to approximate discrete-time nonlinear CDNs with the lower and upper membership functions (MFs) to capture nonlinear parameters. Secondly, both the $H_{\infty }$ robust performance and the $H\text{\_}$ fault sensitivity index are proposed to minimize the effect of external disturbance and maximize that of some faults on the generated residual, respectively. Moreover, based on the lower and upper MFs, the $H\text{\_}$ /$H_{\infty }$ fault detection observer mechanism consisting of IT2 T–S observers and residual systems is designed to detected some faults, which can trigger alarm by evaluation function when fault occurs. Finally, the numerical result of the presented method is shown by applying two simulation examples, which show the effectiveness of the proposed method.