Output regulation for discrete-time nonlinear time-varying delay systems: an LMI approach

In this article, the Takagi-Sugeno (T-S) fuzzy model approach is extended to the stability analysis, control and output regulation design for discrete-time nonlinear systems with time-varying delay. The T-S fuzzy model with varying-time delay are presented and the stability conditions are derived from Lyapunov approach. We also present a stabilization approach and output regulation for nonlinear time delay systems through fuzzy state feedback and fuzzy observer-based like controller. Sufficient conditions for the existence of fuzzy state feedback and integral gain with fuzzy observer gain are derived through the numerical solution of a set of linear matrix inequalities. A numerical simulation example is given to verify the output tracking performance of the proposed methods.