Fault Detection for Networked Control Systems with Two-channel
Packet Dropouts using Delta Operator
Yinshuang Zhang, Duanjin Zhang
School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China
E-mail:djzhang@zzu.edu.cn
Abstract: This paper addresses the problem of fault detection for networked control systems (NCSs) with two-channel packet
dropouts and time-varying delays via delta operator. Packet dropouts exist in both channels from sensors to controllers and
from controllers to actuators, and utilize two independent Bernoulli random variables to represent it. Then the system with
packet dropouts and time-varying delays is modeled as a networked switched system. A design scheme of fault detection filter
is proposed under an arbitrary switching law. Furthermore, sufficient conditions that the switched system is exponentially sta-
ble in the mean-square sense are developed by means of linear matrix inequalities (LMI), Lyapunov-Krasovskii functional and
average dwell-time (ADT) approach. The minimal H
disturbance attenuation level is also achieved. Finally, a numerical ex-
ample is given to illustrate the effectiveness of the proposed method.
Key Words: Networked control systems, fault detection, packet dropouts, time-varying delays, delta operator
1 Introduction
NCSs are feedback systems for which the communica-
tion between sensors, controllers and actuators is supported
by a shared communication network. Compared with tradi-
tional control systems, NCSs have some advantages, such
as information sharing, low cost, high flexibility, which
aroused widespread concerns [1-3]. Due to the introduction
of communication network, some new problems inevitably
occur during data transmission, for instance packet drop-
outs, time delays, uncertainties, etc. [4-5].
In addition, packet dropouts, time delays, and uncertain-
ties may lead to the change of system parameters and even
the whole system structure instantaneously, and then show
multiple characteristics. This feature cannot be described
by traditional system model. However, switched systems
that consisted of a set of subsystems can solve the above
problems; thus it is necessary to utilize switched systems
theory to analyze NCSs [6].
On the other hand, some new progresses have been ob-
tained in the research of NCSs fault detection. The fault
detection problem for uncertain system with limited com-
munication and packet dropouts was presented in [7].
Co-design of fault detection and control for networked
switched systems with time-varying delays was investi-
gated in [8]. Fault detection for switched positive systems
under successive packet dropouts was
concerned in [9].
Furthermore, discrete-time system model formulated by
shift operator has a certain gap at high speed sampling
compared with the previous continuous-time systems, and
poles of the discrete-time systems are located at the
boundary of the stable ring, which leads to the instability of
the system. The emergence of delta operator solves these
problems and the sampling period of the system exists in
the discrete-time systems model, which is convenient to
observe the effect of sampling rate on the system perfor-
mance [11].
Some results for delta operator networked switched sys-
tems are still rare. A
fault detection observer
is designed for
positive switched systems with time-varying delays in [12].
*
This work was supported by National Natural Science Foundation of
China under Grant 61471323.
Besides, robust control for a class of uncertain switched
time delay systems was proposed in [13]. Up to now, the
fault detection has not been fully investigated for delta op-
erator networked switched systems with two-channel
packet dropouts and time-varying delays, which motivates
our investigation.
The purpose of this paper is to study the problem of fault
detection for networked system with two-channel packet
dropouts and time-varying delays. The main contributions
can be summarized as follows: 1) the explicit expression of
the desired filter parameters is presented under arbitrary
switching law; 2) the sufficient conditions are given for the
considered system stability; and 3) it is proved that the
systems have H
performance.
2 Problem Statement
The delta operator is defined by [11]
(1)()
() ,
kxk
xk
h
δ
+−
=
where
0h ≥
is sampling period.
Consider the following delta operator networked
switched systems with time-varying delays:
() ()
() () ()
() () ( ())
() () (),
() (), [ ,0],
kk
kkk
M
xk A xk A xk k
uk D dk F f k
x
σθσ
σσσ
θ
φϑθ
δ
ϑϑ
−
=+−+
°
++
®
°
=∀∈
¯
(1)
where
()∈ℜ
n
xk
,
()∈ℜ
p
uk
and
()∈ℜ
m
fk
denote the
system state vector, control input vector,
fault signal, re-
spectively.
()∈ℜ
q
dk
is the external disturbance belonging
to
2
[0, )l +∞
,
()k
θ
is delay which satisfies
()k
θθθ
≤≤
mM
and
θ
m
,
θ
M
are known constants.
()
n
φϑ
∈ℜ
is the vec-
tor-valued initial function.
Switching signal
()k
σ
is a
piecewise constant function of time and takes values in a
finite set
{1, 2 , 3, }
n= "
and
n
denotes the number of
subsystems.
()
kiN
σ
=∈
shows that the i-th subsystem is
activated, and
i
A
,
θ
i
A
,
i
,
i
,
i
are known matrices.
The data transformation from sensor to controller meets
Proceedings of the 37th Chinese Control Conference
Jul
25-27, 2018, Wuhan, China
6404