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TECHNICAL BRIEFS

# Robust Control for Uncertain Takagi–Sugeno Fuzzy Systems with Time-Varying Input Delay

[+] Author and Article Information
Ho Jae Lee

Department of Electrical and Electronic Engineering,  Yonsei University, Seodaemun-gu, Seoul, 120-749, Koreamylchi@control.yonsei.ac.kr

Jin Bae Park

Department of Electrical and Electronic Engineering,  Yonsei University, Seodaemun-gu, Seoul, 120-749, Koreajbpark@control.yonsei.ac.kr

Young Hoon Joo

School of Electronic and Information Engineering,  Kunsan National University, Kunsan, Chonbuk, 573-701, Koreayhjoo@kunsan.ac.kr

J. Dyn. Sys., Meas., Control 127(2), 302-306 (Jul 12, 2004) (5 pages) doi:10.1115/1.1898238 History: Received February 02, 2003; Revised July 12, 2004

## Abstract

A control problem of Takagi–Sugeno fuzzy systems with a time-varying input delay and norm-bounded uncertainties is addressed. The input delay is well-known in making the closed-loop stabilization difficult. A sufficient condition for the robust fuzzy-model-based stabilization is derived based on the Lyapunov–Razumikhin stability theorem, without the assumption of the variation rate on the delay. A constructive design scheme is presented in the form of the iterative convex optimization problem. The effectiveness of the proposed method is demonstrated by a numerical simulation of a nonlinear mass-spring-damper system.

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## Figures

Figure 1

Nonlinear mass-spring-damper system with an input delay

Figure 2

Behavior of the maximal bound of the time delay via the proposed algorithm: τ computed from Step 1 (solid); τ obtained from Step 2 (solid-diamond)

Figure 3

The applied input delay: d(t)=0, t∊[0,3) (s); 0.1689, t∊[3,3.5) (s); 0.4223, t∊[3.5,5) (s); 0.3379 otherwise

Figure 4

Time responses of x(t) by: Ref. 9 without consideration of the input delay (dotted); the proposed method with consideration of the input delay (solid)

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