1 INTRODUCTION
Networked control systems (NCSs) are combination of
computer technology, control technology and network
communication technology. Compared with the traditional
control systems, the NCSs have the advantages of high
reliability, low cost price and easy maintenance, etc [1-2].
There have been many researches subjected to the NCSs,
the main topic of which are network-induced delay, packet
dropout, communication constraints, and time-varying
sampling periods.
With the increasing of size and complexity of NCSs,
higher reliability of control system is required. Due to the
fact that the occurrence of failures will reduce the
performance of the NCSs, it is important to detect the
faults instantly, which will enhance the security and
reliability of the NCSs [3]. Fault detection has become a
research focus in recent years, for example, Meng and
Zhang proposed the approach to robust fault detection for
NCSs by using delta operator and converted the filter
design to H
∞
optimization problem [4]. The design
approach of fault detection for NCSs with uncertain
time-varying network delays was discussed [5-6]. Serdio
et al constructed new data-driven models by input fault
signal to isolate the failure and introduced the concept of
fault detection gap [7]. Yan et al investigated the problem
of the robust fault detection for networked control systems
basedonstateobserver[8].
For NCSs, the existing studies focused on networked
control systems with a constant sample period. However,
in network systems, the network loads and irregular
failures may result in the sampling period fluttering [9-10].
Recently, there are some researches on time-varying
sampling periods. Borges et al used polyhedron systems to
represent the time-varying periods for designing a H
∞
This work is supported by National Nature Science Foundation of
China under Grant 61471323 and the Key Program of Science
Technology of Education Department of Henan of China under Grant
14A120004.
controller of NCSs [11]. Zhang et al designed a
state-feedback controller satisfied the H
∞
performance for
NCSs with variable sampling periods by using parameter-
uncertain methods [12]. The problem of designing
observer-based fault detection filter for NCSs with active
varying sampling periods was discussed in [13]. Li et al
transformed the NCSs with variable sampling periods into
dynamic interval systems with Taylor formula [14].
Kumiawan et al designed a robust repetitive controller to
compensate the time-varying periodic signal in a known
range. The uncertainty of the sampling periods may lead to
new challenges for fault detection, which motivated this
work.
In this paper, the fault detection issue for NCSs with
uncertain time-varying sampling periods and network
delays is considered. Assuming that the sampling period is
an uncertain value in an effective range, the residual
systems can be modeled as parameter-uncertain systems.
By using the stability theory and constructing a new
Lyapunov function, the sufficient conditions for designed
fault defection filter will be derived in terms of linear
matrix inequalities approach. A numerical example is
provided to indicate the effectiveness of the proposed
method.
2 PROBLEM STATEMENT
Nation:
n
R
represent the n-dimensional euclidean space,
and the superscript
T
expresses the matrix transpose. For a
matrix
A
and two symmetric
CB,
,
!
∀
#
∃
CA
B *
* is the entries implied by symmetry, and
I
is an identity
matrix.
Considering a continuous time linear system as following
%&
∋
(
)
∗∗+
∗∗,∗∗+
)()()()(
)()()()()(
tFftDwtCxty
tEftwBtuBtButAxtx
w
(1)
where
n
Rtx −
is the state vector,
m
Rtw −
is the input
disturbance vector,
s
Rt
−
is the fault vector,
p
Rt
−
Fault Detection for Networked Control Systems with Uncertain
Time-varying Sampling Periods
Yu Cao, Minglei Gao, Duanjin Zhang.
School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China
E-mail: djzhang@zzu.edu.cn
Abstract: The problem of fault detection for networked control systems with uncertain time-varying sampling periods is
investigated. Considering the factors of the network delays and uncertainty of the sampling periods, the residual systems
can be modeled as parameter-uncertain systems. A new filter for the parameters-uncertain systems is developed in view
of the robust fault detection approach. The sufficient conditions of asymptotic stability for the residual systems with H
∞
performance are given with Lyapunov function technique and linear matrix inequalities (LMIs). The designed filter can
guarantee the sensitivity of the residual signal to failures and robustness to the external disturbances of the residual
systems. The effectiveness of the proposed method will be illustrated by a numerical example.
Key Words: Networked control systems, Fault detection, Uncertain sampling periods, Linear matrix inequalities
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978-1-4673-9714-8/16/$31.00
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2016 IEEE