Applied
Soft
Computing
30
(2015)
400–411
Contents
lists
available
at
ScienceDirect
Applied
Soft
Computing
j
ourna
l
ho
me
page:
www.elsevier.com/locate
/asoc
Event-triggered
controller
design
of
nonlinear
discrete-time
networked
control
systems
in
T-S
fuzzy
model
Songlin
Hu
a,b
,
Dong
Yue
b,∗
,
Chen
Peng
c
,
Xiangpeng
Xie
b
,
Xiuxia
Yin
d
a
College
of
Automation,
Nanjing
University
of
Posts
and
Telecommunications,
Nanjing
210023,
PR
China
b
Institute
of
Advanced
Technology,
Nanjing
University
of
Posts
and
Telecommunications,
Nanjing
210023,
PR
China
c
School
of
Mechatronic
Engineering
and
Automation,
Shanghai
University,
Shanghai
200072,
PR
China
d
Department
of
Mathematics,
School
of
Science,
Nanchang
University,
Nanchang,
Jiangxi
330031,
PR
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
10
April
2012
Received
in
revised
form
18
November
2014
Accepted
23
January
2015
Available
online
2
February
2015
Keywords:
Networked
control
systems
Takagi-Sugeno
(T-S)
fuzzy
model
Event-triggered
communication
scheme
Communication
delays
Co-design
algorithm
a
b
s
t
r
a
c
t
This
article
is
concerned
with
event-triggered
fuzzy
control
design
for
a
class
of
discrete-time
nonlin-
ear
networked
control
systems
(NCSs)
with
time-varying
communication
delays.
Firstly,
a
more
general
mixed
event-triggering
scheme
(ETS)
is
proposed.
Secondly,
considering
the
effects
of
the
ETS
and
com-
munication
delays,
based
on
the
T-S
fuzzy
model
scheme
and
time
delay
system
approach,
the
original
nonlinear
NCSs
is
reformulated
as
a
new
event-triggered
networked
T-S
fuzzy
systems
with
interval
time-varying
delays.
Sufficient
conditions
for
uniform
ultimately
bound
(UUB)
stability
are
established
in
terms
of
linear
matrix
inequalities
(LMIs).
In
particular,
the
quantitative
relation
between
the
bound-
ness
of
the
stability
region
and
the
triggering
parameters
are
studied
in
detail.
Thirdly,
a
relative
ETS
is
also
provided,
which
can
be
seen
as
a
special
case
of
the
above
proposed
mixed
ETS.
As
a
difference
from
the
preceding
results,
sufficient
conditions
on
the
existence
of
desired
fuzzy
controller
are
derived
to
ensure
the
asymptotic
stability
of
the
closed-loop
system
with
reduced
communication
frequency
between
sensors
and
controllers.
Moreover,
a
co-design
algorithm
for
simultaneously
determining
the
gain
matrices
of
the
fuzzy
controller
and
the
triggering
parameters
is
developed.
Finally,
two
illustrative
examples
are
presented
to
demonstrate
the
advantage
of
the
proposed
ETS
and
the
effectiveness
of
the
controller
design
method.
©
2015
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
Control
systems
in
which
the
different
components
(i.e.,
sensors,
controllers,
and
actuators)
are
physically
distributed
at
differ-
ent
locations
and
connected
through
a
shared
communication
networks
are
called
networked
control
systems
(NCSs).
Low
cost,
easy
maintenance,
and
system
flexibility
have
dramatically
stim-
ulated
the
use
of
wired
or
wireless
shared
networks
in
a
great
number
of
real
world
applications,
for
example,
sensor
networks,
remote
surgery,
and
intelligent
transportation
systems
[17].
How-
ever,
although
NCSs
have
a
distinct
advantage
over
the
tranditional
point-to-point
control
systems,
the
introduction
of
communica-
tion
networks
in
control
loops
brings
some
challenging
problems
such
as
network-induced
delays
and/or
packet
dropouts,
which
may
degrade
system
performance
or
even
cause
instability
[58].
In
the
past
decade,
how
to
deal
with
these
typical
issues
in
NCSs
∗
Corresponding
author.
E-mail
address:
medongy@vip.163.com
(D.
Yue).
has
become
an
active
research
area,
and
a
number
of
important
results
on
modeling,
control,
and
opimization
of
NCSs
have
been
reported
in
the
existing
literature.
According
to
the
controlled
plants
in
the
published
work,
the
results
can
be
simply
classi-
fied
into
two
types:
some
results
are
focus
on
linear
NCSs,
see,
for
example,
[11,12,30,35,41,42,45–49,52,57];
others
are
for
non-
linear
NCSs,
see,
for
example,
[5,8,13,16,18,23,40,54,55].
It
should
be
pointed
out,
however,
that
these
pieces
of
work
are
based
on
a
common
assumption
that
the
sensor
is
time-triggered
(or
periodic-
triggered),
which
implies
that
all
the
sensor
measurement
need
to
be
transmitted
to
controller
through
communication
networks
at
a
fixed
rate
regardless
of
the
state
of
the
system
to
be
controlled
[32].
In
fact,
in
some
cases,
there
is
no
need
to
transmit
the
measurement
signal
to
controller
node
for
computation,
see,
for
example,
when
the
states
of
the
controlled
plant
are
close
to
equilibrium
point,
since
the
effect
of
the
sensor
measurement
signal
on
system
per-
formance
become
small
during
the
steady
stage
of
state.
Therefore,
in
the
time-triggered
transmission
framework,
some
redundant
measurement
signal
may
be
transmitted,
which
leads
to
inefficient
utilization
of
the
limited
network
resources.
http://dx.doi.org/10.1016/j.asoc.2015.01.041
1568-4946/©
2015
Elsevier
B.V.
All
rights
reserved.
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