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Research Papers

# New Stability Criteria for Stochastic Takagi–Sugeno Fuzzy Systems With Time-Varying Delays

[+] Author and Article Information
K. Mathiyalagan, S. Marshal Anthoni

Department of Mathematics,
Anna University-Regional Centre,
Coimbatore 641 047, India

R. Sakthivel

Department of Mathematics,
Sungkyunkwan University,
Suwon 440 746, South Korea;
Department of Mathematics,
Sri Ramakrishna Institute of Technology,
Coimbatore 641 010, India
e-mail: krsakthivel@yahoo.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 15, 2011; final manuscript received November 8, 2013; published online December 16, 2013. Assoc. Editor: Sean Brennan.

J. Dyn. Sys., Meas., Control 136(2), 021013 (Dec 16, 2013) (9 pages) Paper No: DS-11-1390; doi: 10.1115/1.4026013 History: Received December 15, 2011; Revised November 08, 2013

## Abstract

This paper is concerned with the asymptotic stability issue for a class of stochastic Takagi–Sugeno (TS) fuzzy systems with time-varying delays. Then, by utilizing a delay-fractioning method, the stochastic analysis theory combined with the matrix inequality technique, a new set of sufficient condition in terms of linear matrix inequalities is presented which ensures the asymptotic stability of the stochastic TS fuzzy systems with time-delays. The results obtained in this paper are delay-dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results.

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## References

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## Figures

Fig. 1

Membership functions for Example 4.1

Fig. 2

Trajectories of state variable x(t) of the stochastic fuzzy system for k = 1 and k = 2 with time-delay h2 = 2.26

Fig. 3

Trajectories of state variable x(t) of the fuzzy system without stochastic effects for k = 1 and k = 2 with time-delay h2 = 3.48

Fig. 4

Trajectories of state variable x(t) of the stochastic fuzzy system with time-delay h = 2.79 for k = 1 and k = 2

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