Xian-Ming Zhang and Qing-Long Han. Centre for Intelligent and Networked Systems, Central Queensland University, Rockhampton QLD 4702, Australia.
A novel stability criterion for networked control systems using a new bounding technique Xian-Ming Zhang and Qing-Long Han Centre for Intelligent and Networked Systems, Central Queensland University, Rockhampton QLD
4702, Australia
Email: {q.han.x.zhang}@cqu.edu.au
Abstract-This paper is concerned with the stability of net worked control systems in the discrete-time domain. A new bounding technique is proposed to estimate some finite-sum terms appearing in the forward difference of the chosen Lyapunov func tional. This new bounding technique can provide tighter upper bounds for some finite-sum terms and avoid overly bounding for the finite-sum terms. Then a novel delay-dependent stability
Controller
criterion is derived by using this new bounding technique. Compared with some existing stability criteria in the published literature, the novel stability criterion is proven theoretically to
Fig. l.
A networked control system
be less conservative and is shown to be of smaller numerical complexity.
can adjust its output with the current stored control signal only
I. INTRODUCTION During the past two decades, networked control systems (NCSs) have become an active research topic due to its wide range of applications in many areas
[1]. It is known that
network-induced delays and packet dropouts are unavoidable in an NCS, and they are commonly regarded as main factors that degrade the system performances or even make the system unstable. Up to date, the study on the stability of NCSs has been attracting interests of many researchers in the area of
on each sampling instant. Under these settings, it is clear to see that at the sampling instant
approaches. To mention a few, by using a continuous-time NCS model, stability analysis was made in
[2] and [3]; by
employing a discrete-time NCS model, stability and stabiliza tion were investigated in
the logic ZOH updates
Fx(ikTs),
with which
the physical plant is driven. Since the transmission delays are unavoidable in an NCS, we have
ik
0, (3(k) > 0, and d1 < d(k) < d2. From (15) and (16), it is clear that
and
[14], and will be of smaller numerical complexity than those [10]-[13]. The novel stability criterion can also provide a
larger admissible maximum upper bound of the time-varying time-delay, which is confirmed by two numerical examples. II. A NOVEL STABILITY CRITERION In this section, we will establish a novel delay-dependent stability criterion for the system
(3)
with
(2).
To begin with, a
new lemma is introduced, which is useful for estimating some finite-sum terms appearing in the forward difference of the chosen Lyapunov functional.
d(k) sat d1 and d2 being positive integers. For vector function w : {k - d2, ... ,k - d1 - I} ---7 jRm and m x m real symmetric matrices WI, W2 and real matrix M, Lemma
isfies
d1
2: Suppose that the time-varying function
n x n
0, SI
>
0, S2
real matrix
Z
>
such
R2 Z ] 0 [ZT R2 -
(28)
1 + 2 + 3 < 0
(29)
Proof
Taking the forward difference of
along the solution of
(3)
V (k)
in
(25)
yields
where
(25)
k-l
>
For this purpose, choose
the Lyapunov functional candidate as
V2(k):=
n x n
dl and d2 satisfying 0
