Neurocomputing 260 (2017) 257–264
Contents lists available at ScienceDirect
Neurocomputing
journal homepage: www.elsevier.com/locate/neucom
Design and analysis of H
∞
filter for a class of T-S fuzzy system with
redundant channels and multiplicative noises
R
Sunjie Zhang
a , ∗
, Derui Ding
a , b
, Guoliang Wei
a
, Jingyang Mao
a
, Yurong Liu
c , d
,
Fuad E. Alsaadi
d
a
Engineering Research Center of Optical Instrument and System, Ministry of Education, Shanghai Key Lab of Modern Optical System, University of Shanghai
for Science and Technology, Shanghai 20 0 093, China
b
School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, VIC 3122, Australia
c
Department of Mathematics, Yangzhou University, Yangzhou 225002, China
d
Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
a r t i c l e i n f o
Article history:
Received 15 March 2017
Revised 11 April 2017
Accepted 26 April 2017
Available online 13 May 2017
Communicated by Bo Shen
Keywords:
H
∞
filtering
T-S fuzzy systems
Redundant channels
Multiplicative noises
a b s t r a c t
This paper investigates the design and analysis problem of H
∞
filter for a class of nonlinear systems
based on T-S fuzzy models with both multiplicative noises and redundant channels, which are governed
by a set of Bernoulli distributed white sequences. The packet dropout’s probability of the i -th channel
depends on random Bernoulli variables. The aim of this study is to design and analyze an H
∞
filter that
can stabilize the T-S fuzzy filtering error dynamics. By utilizing both Lyapunov functional approach and
stochastic analysis technique, we establish some sufficient conditions such that the addressed system is
asymptotically stable in the mean square with a given H
∞
performance. The needed filtering parame-
ters are obtained by making use of the matrix inequalities’ solution. In the end, an example is given to
demonstrate the effectiveness and usefulness of the proposed filtering approach.
©2017 Elsevier B.V. All rights reserved.
1.
Introduction
The theory of fuzzy logic has been recognized to be useful in
solving control or filtering problems for lots of complex nonlin-
ear systems. Therefore, it has received considerable research at-
tention (see e.g. [9,10,19,21,22] , and the references therein). Among
different types of fuzzy models adopted to approximate or repre-
sent a nonlinear system, the T-S fuzzy model, proposed by Tak-
agi and Sugeno and described by fuzzy IF-THEN rules, has gained
a lot of public attention It illustrates the local rule for each local
area with a linear equation and then achieves global nonlinear-
ity based on local linearity by fuzzy inference, or say, some simple
linear systems can be used to approximate a nonlinear system via
the determined membership functions. In a nutshell, with fuzzy IF-
THEN rules, the nonlinear system can be described by a T-S fuzzy
model. Therefore, T-S fuzzy model has a better approximation
R
This work was supported in part by the National Natural Science Foundation
of China under Grants 61603255 , 61573246 , 61374039 and 61374010 , the Shanghai
Rising-Star Program under Grant 16QA14030 0 0, the Program for Capability Con-
struction of Shanghai Provincial Universities under Grant 15550502500, and the
China Postdoctoral
Science Foundation Grant 2016M590369 .
∗
Corresponding author.
E-mail address: zhang_sunjie@usst.edu.cn (S. Zhang).
performance. Because a solution scheme can be provided through
incomplete knowledge of the plant, it is a great technique in
practice.
The issue of filter design has long been a basic problem in con-
trol field and thus has gained much research interests (see e.g.
[11–14,17,23–25,27] ). The aim of the filtering is to estimate the dy-
namical system’s states from measurement outputs that may pos-
sibly be disturbed by all kinds of noises, which are inevitable in
real-world systems [3] . Over the past several decades, in order to
guarantee certain robustness of the system with parameter uncer-
tainty, the H
∞
filtering method has been widely employed. It is
worth mentioning that there is an increasing interest in the fuzzy
H
∞
filtering issue based on the T-S model (see e.g. [6,7,16,20] ). On
the other hand, the control and filtering problems for T-S fuzzy
systems with multiplicative noises have also drawn much research
attention, since several nonlinear systems could be approximated
by models with multiplicative noises, and multiplicative noises
have an effect on the stability. So far, there have been some prelim-
inary attempts to solve the control and filtering problems for T-S
fuzzy systems with multiplicative noises. In [26] , the stochastic dis-
turbances in the T-S fuzzy model are multiplicative noises, namely,
state-dependent noises. The stabilization problems have been re-
searched in [4] for a kind of T-S fuzzy system with multiplicative
noises. However, only a few research results have been proposed to
http://dx.doi.org/10.1016/j.neucom.2017.04.040
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