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Research Papers

# Robust State Feedback H∞ Control for Discrete-Time Fuzzy System With Random Delays

[+] Author and Article Information
R. Sakthivel

Department of Mathematics,
Sungkyunkwan University,
Suwon 440-746, Republic of Korea
e-mail: krsakthivel@yahoo.com

A. Arunkumar, K. Mathiyalagan

Department of Mathematics,
Anna University Regional Campus,
Coimbatore 641 046, India

Ju H. Park

Department of Electrical Engineering,
Yeungnam University,
Kyongsan 38541, Republic of Korea
e-mail: jessie@ynu.ac.kr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 28, 2013; final manuscript received March 10, 2017; published online June 5, 2017. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 139(8), 081017 (Jun 05, 2017) (11 pages) Paper No: DS-13-1419; doi: 10.1115/1.4036237 History: Received October 28, 2013; Revised March 10, 2017

## Abstract

This paper investigates the problem of robust stabilization for a class of discrete-time Takagi–Sugeno (TS) fuzzy systems via input random delays in control input. The main objective of this paper is to design a state feedback $H∞$ controller. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust $H∞$ controller. In particular, the effect of both variation range and distribution probability of the time delay is taken into account in the control input. The key feature of the proposed results in this paper is that the time‐varying delay in the control input not only dependent on the bound but also the distribution probability of the time delay. The obtained results are formulated in terms of LMIs which can be easily solved by using the standard optimization algorithms. Finally, a numerical example with simulation result is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed result.

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## Figures

Fig. 4

Simulation of random variable δ(k) and time‐varying delay τ(k) for nominal model

Fig. 1

State trajectories of fuzzy system (7) without control when η=1, η=2

Fig. 2

State trajectories of fuzzy system (7) with control when η=1, η=2

Fig. 3

Control trajectories of fuzzy system (7) when η=1, η=2

Fig. 5

State trajectories of the uncertain fuzzy system (6) without control when η=1, η=2

Fig. 6

State trajectories of the uncertain fuzzy system (6) with control when η=1, η=2

Fig. 7

Control trajectories of the uncertain fuzzy system (6) when η=1, η=2

Fig. 8

Simulation of random variables δ(k) and time‐varying delays τ(k) for the system (6)

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