New sufficient conditions for robust H∞ fuzzy hyperbolic tangent control of uncertain nonlinear systems with time-varying delay

Authors:
Huaguang Zhang;Xinrui Liu;Qingxian Gong;Bing Chen
Affiliations:
School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, PR China and Key Laboratory of Integrated Automation of Process Industry (Northeastern University ...;School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, PR China;School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, PR China and Changchun Institute of Technology, Changchun, Jilin 130012, PR China;Institute of Complexity Science, Qingdao University, Qingdao 266071, PR China
Venue:
Fuzzy Sets and Systems
Year:
2010

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Abstract

This paper considers the delay-dependent robust H"~ control problem based on fuzzy hyperbolic model (FHM) for a class of uncertain nonlinear systems with time-varying delay. Firstly, FHM modeling method is presented for uncertain nonlinear systems with time-varying delay. Secondly, the new delay-dependent sufficient condition for the existence of a state feedback fuzzy hyperbolic tangent controller is proposed in terms of linear matrix inequalities (LMIs) by constructing a novel Lyapunov-Krasovskii functional. The robust FHM-based control law can guarantee that the closed-loop system is robustly asymptotically stable with a prescribed H"~ index. As more information of the FHM and the size of time-delay are taken into account, the proposed conditions are new and less conservative. Finally, three illustrative examples are given to show the effectiveness of using FHM-based controllers.