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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS 1
Dissipative Fuzzy Filtering for Nonlinear Networked
Systems With Limited Communication Links
Ziran Chen, Baoyong Zhang , Yijun Zhang, and Zhengqiang Zhang
Abstract—This paper aims to design a dissipative fuzzy filter
for a class of discrete-time nonlinear networked systems. In order
to adopt the limited communication links, we employ an event-
triggered scheme to reduce the number of transmitted data in
the network by preventing the unnecessary ones from releasing.
Due to the digital channel, the data to be transmitted should be
quantized and a logarithmic quantizer is employed. Then, when
the part of released data is transmitted in the network, data losses
is captured by a Bernoulli process. Consequently, the uncomplete
data sequence is compensated by the buffer and then send to the
filter. During this process, a new random series is developed to
help constructing the filtering systems. Thus, a novel method is
presented to guarantee the filter error system to be dissipative
based on the T–S fuzzy model approach. Finally, an example
concerned with Henon mapping system is provided to verify the
validity of the proposed design method.
Index Terms—Data losses, dissipative filter, event-triggered
scheme, networked systems, T–S fuzzy model.
I. INTRODUCTION
N
ETWORKED systems represent a class of systems whose
components are geographically distributed in different
areas [1]–[7]. Different from traditional point-to-point con-
nected systems [8]–[11], the networked systems are closed via
network channels which are usually not reliable. Therefore,
some issues, such as data losses, data quantization, and trans-
mission delay should be taken into account. By considering
these issues, a networked control system was designed in [12]
based on a dynamic output-feedback controller. In [13], a
distributed filter is designed for fuzzy delay systems under
networked links with packet dropouts and redundant chan-
nels. In [14], a unified model was proposed to describe
Manuscript received June 26, 2017; revised September 20, 2017; accepted
October 19, 2017. This work was supported in part by the Natural Science
Fund for Distinguished Young Scholars of Jiangsu Province under Grant
BK20150034, in part by the National Natural Science Foundation of China
under Grant 61473151, Grant 61473152, and Grant 61473171, in part by
the Qing Lan Project, in part by the Shandong Provincial Natural Science
Foundation for Distinguished Young Scholars under Grant JQ201515, and in
part by the Taishan Scholarship Project of Shandong Province under Grant
tsqn20161032. This paper was recommended by Associate Editor H. Li.
(Corresponding author: Baoyong Zhang.)
Z. Chen, B. Zhang, and Y. Zhang are with the School of Automation,
Nanjing University of Science and Technology, Nanjing 210094, China
(e-mail: chenziran0719@gmail.com; baoyongzhang@njust.edu.cn; zhangyi-
jun@njust.edu.cn).
Z. Zhang is with the School of Electrical Engineering and Automation,
Qufu Normal University, Rizhao 276826, China (e-mail: qufuzzq@126.com).
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/TSMC.2017.2770161
the phenomenon of data loss, transmission rate reduction,
and signal quantization for a class of switched systems.
It is now known that the reliability problems, such as
network induced delay and data loss for continuous-time
systems can be addressed by the well developed delay-
system approach [15], [16]. And the data loss phenomenon
in discrete-time networked systems can be captured via
probability-distribution function method [17].
Apart from the reliability, another important issue should be
considered is the utilization of the network resource. There are
two approaches to save the limited network resource, one is
to reduce the data size and the other is to decrease the num-
ber of transmitted data packets. The former can be realized
by logarithmic quantizer as presented in [18] and [19]. For
the latter, event-triggered schemes are always adopted instead
of time-triggered schemes. In time-triggered scheme, all the
sampled data are adopted for system synthesis without the
consideration of efficiency of communication resources. Such
a drawback could be overcome by applying the event-triggered
scheme to prevent unnecessary data from releasing to the
network [20]–[28]. For example, in [20], an event-triggered
mechanism is designed for a class of fuzzy control systems
with transmission delay by which the utilization of network
resources is improved.
It is worth mentioning that, under event-triggered scheme,
data loss model is not easy to be constructed by existing
approaches due to the inconsecutive data sequence. Therefore,
few result has been proposed to handle the problem. In [29],
the problem in continuous-time systems is solved under the
constraint of a given maximum allowable number of suc-
cessive data losses. Additionally, the probability-distribution
function approach is widely used to deal with data losses
in discrete-time systems. In this method, data losses on
every transmitted data packages can be described by inde-
pendent Bernoulli trials. And all of them can constitute a
Bernoulli distribution. However, under the influence of event-
triggered scheme, only part of the data is released to the
network, the Bernoulli distribution method is not valid for
this situation. Therefore, new methods need to be devel-
oped for this problem. This is one of the motivations of this
paper.
On the other hand, the nonlinear systems have got consider-
able progress [30]–[33]. In which the T–S fuzzy model-based
approach has gotten widely use due to its high estimation
ability of nonlinearities [34]–[36]. For example, in [37], T–S
fuzzy model is employed to describe the nonlinear systems
and correspondingly a distributed fuzzy static output feedback
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