**1. Introduction**

The networked systems have been widely used because of these many advantages, their simple physical structure, reduced integration costs, resource sharing, suitable for installation, expansion and maintenance [1,2]. In order to satisfy the development of aerospace and smart manufacturing, the networked systems have increasingly strong nonlinearity, uncertainty and complexity [3,4]. New challenges are brought to the control field to deal with problems such as delay, data packet loss and network bandwidth limitation caused by network introduction [5–9]. With the development of nonlinear networked systems, it needs new performance indexes including standard interface modularization, high reliability, high stability, and so on [10,11].

Fuzzy control is an effective tool for solving nonlinear problems linearization [7,12]. Fault diagnosis (FD) technology plays a vital role in improving the reliability and safety of complex engineering systems [13,14]. The task of fault diagnosis of the networked system is to transmit the input and output data of the system to the fault diagnosis unit through the network, so as to ensure that the stable operation of the system without fault occurs [6]. The FD methods of networked systems are proposed based on the fuzzy model [7,15,16]. However, there are bad situations under time-triggered FD such as unnecessary data transmission, increased network burden, data loss, and greater network

**Citation:** Lu, Z.; Zhang, C.; Xu, F.; Wang, Z.; Wang, L. Fault Detection for Interval Type-2 T-S Fuzzy Networked Systems via Event-Triggered Control. *Machines* **2022**, *10*, 347. https://doi.org/ 10.3390/machines10050347

Academic Editor: Ahmed Abu-Siada

Received: 27 March 2022 Accepted: 6 May 2022 Published: 8 May 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

delay [8]. The event-triggered mechanism has irreplaceable advantages in the network resource-constrained system. The research on fault diagnosis technology of networked systems with event-triggered mechanisms has received extensive attention from international scholars, which has become a hot research issue in the academic community of automatic control and produced many valuable research results [8,9,15–32].

Different event triggering methods are studied such as the adaptive event-triggering mechanism [5,10,22,23,27,29,32], the dynamic event triggering mechanism containing internal dynamic variables [19,28,31], the event triggering mechanism designed by improving constant thresholds [8,15,16,20,21,25,26]. The fault filtering problem of NCSs with interval time-varying time lags is studied by using the fuzzy fault detection filter with a generic structure [17]. The authors in [22] propose a novel adaptive event-triggered fault detection approach for Markov jump systems, wherein the transition probabilities are not required to be fully known. The problem of troubleshooting networked systems subject to multiple factors is discussed [21,23,25,28,30]. The problem of fault detection for stochastic nonlinear generalized networked systems is studied, which is subject to network delay, packet loss, and asynchronous premise variables [23]. Fault diagnosis problems of NNSs with communication channels are subject to limited bandwidth and random data loss are investigated. Time-varying delay, dynamic event triggering mechanism, random nonlinearity and simultaneous packet loss are considered in building a unified fault detection dynamic model moment, which is used to solve the fault detection problem [28]. The dissipative stabilization problem is solved by considering the delay and external disturbance [30].

The existing research has been extensive. However, the complexity of real systems can no longer be described by simple models. For instance, the membership functions approaches have been proposed based on the restriction that the membership functions of the descriptive model of the systems [15,16,21]. When this issue is considered, the general T-S fuzzy modeling scheme cannot achieve the desired results [15]. The IT2 fuzzy model was developed because of its good proxy for nonlinear systems with parameter uncertainty [29–37]. The problem of the FD filtering method is proposed with event-based, which is the application in IT2 fuzzy theory under the framework of networked timedelay control systems [29]. Event-triggered dissipation-based control is investigated by using the IT2 T-S fuzzy theory to describe uncertain nonlinear networked systems [30]. The nonlinear networked system with parameter uncertainty is studied under the eventtriggered mechanism with adaptive discrete *H*∞ fuzzy filtering described by IT2 T-S fuzzy model [32]. In [33–38], the FD fighting design, impulse control and discrete control based on the IT2 fuzzy model are studied. Interval two-type theory is being recognized and studied by more and more scholars [39,40]. Expanding the application scope of event-driven technology in the IT2 fuzzy control system is the first motivation for writing this paper.

Then, the FD methods for fuzzy systems have been proposed without considering the problems of nonlinear perturbation and transmission-limited [13,14]. Reducing the conservativeness of existing results and redundancy in design is a difficult issue of academic concern. In summary, solutions to event-driven FD problems are important for NNSs subject to uncertainties, perturbation, and network-induced delays. The main contributions of the paper as follows:


The rest of this paper is structured as follows. An IT2 fuzzy fault residual system is given based on the IT2 fuzzy networked control system model, event-triggered scheme,

and fault diagnosis mechanism in Section 2. Section 3 is the focus of the article and is intended to discuss and clarify the stability analysis and the design of the filter for the fault residual system. Section 4 conducts simulations and discusses the validity of the proposed method. The full paper is summarized, and further research directions are given in Section 5.

Table 1 shows the abbreviations and notations used in this paper.

**Table 1.** Explanation of abbreviations and notations.

