H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control


  • Xizheng Zhang Hunan University P.R.China, 410082 Changsha, Yuelushan, and Hunan Institute of Engineering P.R.China, 411104 Xiangtan, 88 Fuxing East Road
  • Yaonan Wang Hunan University P.R.China, 410082 Changsha, Yuelushan
  • Xiaofang Yuan Hunan University P.R.China, 410082 Changsha, Yuelushan


sliding mode control, T-S fuzzy model, time-delayed system, H∞ control


This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with state delay, which can be represented by a Takagi-Sugeno (TS) model with uncertainties. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H∞ technique such that the robust asymptotically stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified switching surface is proven. Simulation results show the validity of the proposed method.


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