2016 16th International Conference on Control, Automation and Systems (ICCAS 2016)
Oct. 16-19, 2016 in HICO, Gyeongju, Korea
1. INTRODUCTION
As is well known, Takagi-Sugeno (T-S) fuzzy system
is a powerful tool to approximate the nonlinear systems
by weighting sum of a family of local fuzzy IF-THEN
rules. Many scientists and engineers have devoted
themselves to the research of filtering and control
problems for the T-S fuzzy systems since it was
proposed by Zadeh in 1965, see, for example, stability
analysis [1], reliable control [2], Non-fragile filtering [3]
and the references therein. On the subject of the filtering
problem for T-S fuzzy systems, the
∞
method has
attracted great attention in recent years and many results
have been reported [4-6] because it does not make any
assumptions on the statistical properties of the process
and measurement noises compared with the classical
Kalman filtering method.
Nowadays, one of the most significant trends is the
increasing application of networks in modern dynamical
industrial processes. The so-called networked control
systems (NCSs) have many advantages, such as low
cost, simple installation and maintenance, convenient
system diagnosis and increased system agility. But, due
to the limited bandwidths of the communication
channels, the data packet will be received with delays
even be lost during the transmission through the
network. In this case, traditional filtering results based
on the T-S fuzzy model may not provide a reliable
solution and are not applicable. Many researchers have
denoted themselves to investigating the filtering
problems under the above two important issues of the
NCSs [7-9]. In [7], the robust fault detection problem is
studied for a class of uncertain discrete-time T-S fuzzy
systems with stochastic mixed time delays and
successive packet dropouts. In [8], the distributed fuzzy
filter design problem is concerned with for a class of
sensor networks described by discrete-time T-S fuzzy
systems with time-varying delays and multiple
probabilistic packet losses. In [9], the
∞
fuzzy
filtering problem is investigated for a class of
discrete-time T-S fuzzy systems with randomly
occurring interval time-varying delays, as well as
channel fadings. On the other hand, due to the physical
or technological constraints, the sensor saturation
phenomenon usually occurs in practical industrial
control systems and it is another main factor leads to
poor performance of the controlled systems. The latest
reference [10] studies the
∞
filtering for a class of
discrete T-S fuzzy stochastic systems where the sensor
saturations and missing measurements are concerned
with, but the transmission delay is not considered.
Compared with the well-studied transmission delays and
packet dropouts, the sensor saturation has not been fully
investigated for T-S fuzzy networked systems. This
motivates our current study.
In this paper, we focus on the
∞
filtering problem
for network-based stochastic T-S fuzzy systems. The
measurement output is subject to sensor saturations and
transmitted to the remote filter through the network
links. The considered imperfect transmission
phenomena contain the time delays and packet dropouts
whose random nature is modeled by a group of
Bernoulli distributed white sequences. The main
objective of this paper is to design a full-order
∞
fuzzy filter such that the filtering error dynamics is
asymptotically stable in the mean square and the
disturbance rejection attenuation is constrained to a
prescribed level. The solvability condition of the
designed filter is then expressed in terms of LMIs.
Finally, an illustrative example is given to show the
effectiveness of the proposed method.
2. PROBLEM FORMULATION
Consider the network-based discrete-time nonlinear
system represented by the following T-S model:
∞
Filtering for T-S Fuzzy Systems with Random Multiple Delays and Packet Dropouts
Subject to Sensor Saturations
Xiu-Ying Li
1*
, Yue Xu
1
, and Shu-Li Sun
1
1
Department of Electrical Engineering, Heilongjiang University,
Harbin, 150080, China (xiuxiu4480@sina.com)
Abstract: This paper focuses on the problem of
∞
filter design for a class of Takagi-Sugeno (T-S) fuzzy
network-based systems where the measurement output is subject to the sensor saturations described by sector-
nonlinearity. The investigated issues caused typically in the wireless communication include the multiple and
ounded
transmission delays as well as the consecutive packet dropouts whose random nature is governed by Bernoulli
distributed random variables. A full-order
∞
filter is designed such that, in the simultaneous presence of the multiple
delays and packet dropouts as well as sensor saturations, the filtering error system is asymptotically mean-square stable
and satisfies the prescribed
∞
performance index. A sufficient condition for the existence of such a filter is established
in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate
the effectiveness and the feasibility of the proposed filtering design method.
Keywords:
∞
filter; Packet dropout; Transmission delay; Sensor saturation; Takagi-Sugeno (T-S) fuzzy system.
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