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

摘要

This paper proposes an output tracking control via virtual reference model for a class of nonlinear dis crete-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.