This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON CYBERNETICS 1 Distributed H ∞ Filtering for Switched Stochastic Delayed Systems Over Sensor Networks With Fading Measurements Yun Chen, Zidong Wang , Yuan Yuan , and Paresh Date Abstract—This paper is concerned with the problem of dis- tributed H ∞ filtering for switched stochastic time-delay systems with fading measurements over sensor networks. The underly- ing target plants are subject to fading measurements where the fading rates are described by continuous-time random variables with known statistical properties dependent on the system modes. The adjacency matrices characterizing the topology of the sensor networks are also allowed to be mode-dependent. Based on the multiple Lyapunov functional approach and average dwell-time concept, the distributed H ∞ filter is designed by means of the convex optimization scheme. A dedicated technique is developed via a simple algebraic equality in order to avoid solving a tran- scendental equation used in the existing results. With the designed filter, the error dynamics of the state estimation is guaranteed to have the mean-square exponential stability with a prescribed H ∞ disturbance attenuation level. Finally, a numerical example is used to demonstrate the effectiveness of the method. Index Terms—Average dwell time (ADT), distributed H ∞ fil- tering, fading measurements, sensor networks, switched stochas- tic systems. I. I NTRODUCTION R ECENT years have witnessed a constant research inter- est in the study of wireless sensor networks (WSNs) that are comprised of spatially distributed sensors and normally deployed as environmental monitoring systems [1], [26], [27], [33], [37]. Compared with traditional point-to-point sensing, the WSN takes great advantages in larger coverage, lower Manuscript received December 18, 2017; revised April 1, 2018; accepted June 22, 2018. This work was supported in part by the Research Fund for the Taishan Scholar Project of Shandong Province of China, in part by the Royal Society of the U.K., in part by the Zhejiang Provincial Natural Science Foundation of China under Grant LR16F030003, in part by the National Natural Science Foundation of China under Grant 61473107, Grant U1509205, and Grant 61333009, and in part by the Alexander von Humboldt Foundation of Germany. This paper was recommended by Associate Editor J. Qiu. (Corresponding author: Zidong Wang.) Y. Chen is with the Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China (e-mail: yunchen@hdu.edu.cn). Z. Wang is with the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China, and also with the Department of Computer Science, Brunel University London, Uxbridge UB8 3PH, U.K. (e-mail: zidong.wang@brunel.ac.uk). Y. Yuan is with the Department of Computer Science, Brunel University London, Uxbridge UB8 3PH, U.K. (e-mail: yuan.yuan@brunel.ac.uk). P. Date is with the Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, U.K. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCYB.2018.2852290 cost, better fault tolerance, and ubiquitous operation capabil- ity even under harsh working conditions. On the other hand, it is worth noting that the utilization of WSN also gives rise to new research challenges. As pointed out in [4], two crit- ical yet interdependent challenges resulting from WSNs lie in the efficient networking techniques and the effective signal processing mechanism for coping with the distributed infor- mation. Accordingly, it is not surprising that the distributed filtering (or estimation) over WSNs has recently become one of the most significant research problems in the areas of dis- tributed signal processing and control, and a great number of excellent results have been available in [7], [11], [14], [29], [32], [35], [36], [40], and [44]. In the context of distributed filtering, each sensor node is only capable of obtaining access to its neighboring sensors under a given topology. To provide an estimate, the individual sensor node equipped with a filter employs the measurements provided by both local and neighboring sensors. It is worth mentioning that, with the increase of the scale of the WSN, both limited communication capacity and limited computation resources are likely to lead to undesirable network-induced phenomena (e.g., packet dropouts, communication delays, and fading measurements) which, in turn, result in unpredictable performance degradation for the filters [6], [39], [44]. These identified features of the WSN pose two difficulties for the design of the distributed filters. 1) The complexities resulting from the cou- pling/interdependence of the sensor nodes under a certain topology should be reflected in the design procedure. 2) The network-induced phenomena should be taken into consideration in the design of the distributed filters over WSN. In the past few years, the distributed filtering problem with network-induced phenomena has become a focus of research attracting an ever-increasing interest from both sig- nal processing and control communities [8], [30], [43]. For example, in [44], a distributed multirate fusion estimation method has been designed for the WSN subjected to random packet dropout. In [32], in virtue of the stochastic sampled- data method, a distributed filtering problem has been addressed for the WSN. It is noted that, among various network-induced phenomena [3], [5], [16], the channel fading [13], [20] is gen- erally considered to be unavoidable in the setting of wireless communication that might be caused by a variety of reasons 2168-2267 c  2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.