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

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.

► A Takagi–Sugeno (T–S) fuzzy model represents the discrete-time nonlinear system with time-varying delay.
► 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.
► We allow unknown time-varying delay, ensure robust output tracking, provide relaxed conditions via a three-steps procedure to find observer and controller gain.