Robust output tracking control for discrete-time nonlinear systems with time-varying delay: Virtual fuzzy model LMI-based approach

  • Authors:

  • Tung-Sheng Chiang;Peter Liu

  • Affiliations:

  • Department of Electrical Engineering, Ching Yun University, 320 Zhongli City, Taoyuan, Taiwan;Department of Electrical Engineering, Tamkang University, 25137 Tamsui, New Taipei City, Taiwan

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2012

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Abstract

This paper proposes an output tracking control via virtual reference model for a class of nonlinear discrete-time systems with time-varying delay and disturbance. First, a Takagi-Sugeno (T-S) fuzzy model represents the discrete-time nonlinear system with time-varying delay. Second, a fuzzy observer design estimates immeasurable state. Third, a virtual desired variable (VDV) based tracking controller design guarantees H"~ control performance for the overall system. Using Lyapunov's stability analysis, we obtain sufficient conditions for stability of estimation, control, and robustness. The advantages are as follows: (i) allow unknown time-varying delay; (ii) ensure robust output tracking; (iii) provide relaxed conditions via a three-steps procedure to find observer and controller gain. To verify the theoretical derivation, we carry out numerical simulations on a stirred tank reactor system as an example. Satisfactory results validate the claims.