IFAC PapersOnLine 50-1 (2017) 2989–2994
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2405-8963 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
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10.1016/j.ifacol.2017.08.665
© 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Stability Analysis of Nonlinear Networked
Control Systems via Takagi-Sugeno Fuzzy
Model
Jun Yoneyama
*
*
Aoyama Gakuin University, Sagamihara, Kanagawa, 252-5258 Japan
(e-mail: yoneyama@ee.aoyama.ac.jp).
Abstract: The paper is concerned with stability analysis of nonlinear networked systems
which are described by the Takagi-Sugeno fuzzy systems. In the networked control system,
the information is exchanged with packets through a network where the data packets encounter
delays. The closed-loop system with a controller can be modeled as a fuzzy system with time-
varying delays in sensor and actuator modes. Based on a novel Lyapunov-Krasovskii stability
theorem, the stability analysis problem of a fuzzy system with time-varying delays is considered.
Multiple Lyapunov-Krasovskii function with multiple integral functions allows us to obtain less
conservative conditions for the networked control system to be asymptotically stable. In fact,
this method drastically reduces the conservatism in stability conditions.
Keywords: Fuzzy systems, Intelligent control, Networks, Nonlinear control systems,
Time-delay.
1. INTRODUCTION
Most physical systems are nonlinear and they appear in
many engineering fields. In the past three decades, Takagi-
Sugeno fuzzy model has been widely used for nonlinear
control systems since it can universally approximate or
can exactly describe general nonlinear systems(Lam et al.
(2000), Takagi and Sugeno (1985), and Tanaka and Sugeno
(1992)). In fact, Takagi-Sugeno fuzzy model has played an
important role for nonlinear system analysis and its control
design. The stability of fuzzy systems was investigated in
Lee et al. (2014), Tanaka and Sugeno (1992), Teixiera et
al. (2003), and Tuan et al. (2001). The recent paper by Lee
et al. (2014) gave novel stability conditions but no control
design method was provided there. Fuzzy control theory
has been extended to a class of fuzzy systems with local
nonlinear systems in Yoneyama (2014). Yoneyama (2014)
greatly reduces conservatism in control design conditions.
Such a generalized fuzzy system has been considered, and
stability and stabilizability conditions have been obtained.
However, those conditions are still conservative, and there
is room to improve.
Many results on the state feedback controller design
method have appeared in the literature(for example, Lam
et al. (2000), Precup et al. (2012), Tanaka and Sugeno
(1992), Wang et al. (1996), and references therein.). The
paper by Lam et al. (2000) uses a state feedback parallel
distributed compansator(PDC), whose membership func-
tions are mismatched with local controlled systems, and
gives less conservative stability conditions than those of
Tanaka and Sugeno (1992) and Wang et al. (1996). The
paper by Precup et al. (2012) recently provided a state
feedback control method by iterative technique but still
needs much computational load. The paper by Tanaka et
al. (2007) adopted a descriptor system approach, which re-
duces control design conditions for the state feedback con-
trol design. The paper by Guelton et al. (2009) extended
the descriptor system approach to the case of the output
feedback control design. It is well-known that although
descriptor systems are more complicated than state-space
systems, they have richer structures, which produces less
conservatism in the control design conditions. Those two
papers used a multiple Lyapunov matrix method, which is
a generalization of a common Lyapunov matrix method.
The papers by Li et al. (2016), Marouf et al. (2016), and
Zhang et al. (2007) considered control design problems
for nonlinear networked control systems. Li et al. (2016)
partially introduced a multiple Lyapunov-Krasovskii ma-
trix method for fuzzy systems with time-delay but it
is not a general multiple matrix method. Marouf et al.
(2016) employed a common Lyapunov-Krasovskii function
method with descriptor system approach, which is still
more conservative than a multiple Lyapunov-Krasovskii
matrix method.
In this paper, we consider a nonlinear networked control
system design based on Takagi-Sugeno fuzzy models. First,
we assume a special form of fuzzy feedback controller
and consider the closed-loop system with such a feedback
controller. In order to obtain less conservative stability
conditions, we introduce a new type of multiple Lyapunov-
Krasovskii function, which reduces the conservatism in
our stability condition. Such a new multiple Lyapunov-
Krasovskii function employs an integral of the member-
ship functions of fuzzy systems. A multiple Lyapunov-
Krasovskii function is a natural extension of a common
Lyapunov function. However, since a conventional multiple
Lyapunov-Krasovskii function contains the membership
function, a resulting stability condition depends on the
derivatives of the membership function that is a function of
the premise variables. However, the membership function