L
2
-Gain Control for T-S Fuzzy Systems Over an Event-Triggered
Communication Network Using Delay Decomposition
and Deviation Bounds of Membership Functions
Xinchun Jia
1
•
Junhua Zhao
1
•
Dawei Zhang
1
Received: 27 May 2015 / Revised: 24 November 2015 / Accepted: 10 December 2015
Ó Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016
Abstract This paper is concerned with networked L
2
-
gain control for a T-S fuzzy system over an event-triggered
communication network. Taking an event-triggered com-
munication scheme and network-induced delays into con-
sideration, the networked control system is described by an
asynchronous T-S fuzzy system with an interval time-
varying delay. Due to variation characteristic of network-
induced delays, the interval is decomposed into N subin-
tervals and the jumping among these subintervals is gov-
erned by a Markov chain. A new relaxation method, which
fully utilizes the convexity of normalized membership
functions and the deviation bounds of asynchronous nor-
malized membership functions, is proposed and a
stochastic Lyapunov–Krasovskii functional is constructed
to derive some delay-dependent criteria on L
2
-gain per-
formance analysis and controller design of the asyn-
chronous T-S fuzzy system. An illustrative example is
provided to show that the proposed criteria are of less
conservatism and less computational complexity than some
existing results, and are effective in achieving a prescribed
L
2
-gain performance.
Keywords T-S fuzzy system Event-triggered
communication network Network-induced delay Markov
chain Asynchronous normalized membership functions
1 Introduction
Networked control systems (NCSs) arise in modern
industries as an alternative scenario of traditional point-to-
point wired systems due to the advantages such as flexible
architecture, low cost, high reliability, decreased wiring,
remote control, and extensive potential applications [1–3].
When exchanging information through a communication
network, network-induced delay is inevitable, which has a
negative effect [4–6] and a positive effect [7, 8] on stability
and system performance. As a result, network-induced
delay is a popular and significant issue appealing to many
researchers. According to the network protocols adopted
and the chosen hardware, the characteristic of network-
induced delays occurs frequently in either time-varying or
random way [9]. How to fully utilize the variation char-
acteristic of network-induced delays in modeling, analysis,
and design of an NCS is a crucial issue to be concerned
with. So far, time-varying characteristic [10, 11] and ran-
dom characteristic [12–14] of network-induced delays have
been considered.
As is well known, T-S fuzzy model is effective and
prevalent to approximate many practical nonlinear systems
on any compact set to arbitrary accuracy [15–21]. For
conventional fuzzy control systems, several different con-
trol strategies are proposed, for example, sliding-mode
control [15, 21], state feedback control [18], adaptive fuzzy
control [22–24], and output feedback control [25]. How-
ever, these fuzzy control methods are established for T-S
fuzzy systems in traditional point-to-point wired system
scenarios. The advent of NCS scenarios sparks increasing
technology and methodology research on network-based
control of T-S fuzzy systems. For T-S fuzzy systems in the
NCS scenario, the insertion of a communication network
makes a difference in system modeling, stability analysis,
& Dawei Zhang
zhangdaweisx@sxu.edu.cn
1
School of Mathematical Sciences, Shanxi University,
Taiyuan, China
123
Int. J. Fuzzy Syst.
DOI 10.1007/s40815-015-0127-z