Fuzzy Dynamic Output Feedback Control for T-S Fuzzy Discrete-Time Systems With Multiple Time-Varying Delays and Unmatched Disturbances

This paper addressed the fuzzy dynamic output feedback control problem for a class of nonlinear discrete-time Takagi–Sugeno (T-S) fuzzy systems with multiple time-varying delays and unmatched disturbances. Based on the control input matrix and output matrix, the T-S fuzzy model is employed to approximate the nonlinear discrete-time system. Based on the stochastic system theory and the Bernoulli distribution, the fuzzy dynamic output feedback controller is constructed for the nonlinear discrete-time T-S fuzzy system with multiple time-varying delay and unmatched disturbance. The
$H_{\infty } $
performance analysis is presented, and the cone complementarity linearization algorithm is employed for the stability analysis to deal with the non-convex problem caused by the basis-dependent linear matrix inequalities conditions. Compared with the previous works, the developed controller in this paper is smooth and only uses the system output. The control design conditions are relaxed because of the developed cone complementarity linearization algorithm. The results are further extended to the chemical process case and the mobile robot case. Finally, two simulation examples are performed to show the effectiveness of the proposed methods.