Title: New robust H_∞ control approach for discrete T-S fuzzy time-delay system

Authors: Songtao Zhang; Xiaowei Zhao; Jiantong Zhang

Addresses: School of Management, Harbin University of Commerce, Harbin, Heilongjiang 150028, China ' School of Economics and Management, Tongji University, Shanghai 200092, China ' School of Economics and Management, Tongji University, Shanghai 200092, China

Abstract: A new piecewise Lyapunov-Krasovskii function approach on the stability analysis and the robust H_∞ controller design of the discrete T-S fuzzy time-delay system is studied in this paper. Based on the definition of maximal overlapped-rules group, the systematic design of the fuzzy robust H_∞ controller is investigated via parallel distributed compensation control scheme. And for the closed-loop discrete T-S fuzzy time-delay system, a new sufficient stability condition is proposed. This sufficient condition only requires finding common matrices in each maximal overlapped-rules group. The proposed condition is less conservative and difficult than the common Lyapunov-Krasovskii function approach and the fuzzy Lyapunov-Krasovskii function approach. Lastly, the simulation results show the effectiveness of the proposed approach.

Keywords: T-S fuzzy modelling; time-delay systems; robust control; H-infinity control; stability analysis; controller design; parallel distributed compensation control; simulation; Takagi-Sugeno.

DOI: 10.1504/IJAAC.2015.073488

International Journal of Automation and Control, 2015 Vol.9 No.4, pp.333 - 354

Received: 06 Nov 2014
Accepted: 15 Sep 2015
Published online: 09 Dec 2015 *

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