ℓ₂–ℓ∞ Control of Discrete-Time State-Delay Interval Type-2 Fuzzy Systems via Dynamic Output Feedback

This article investigates the design of the $\ell _{2}-\ell _{\infty }$ dynamic output-feedback (DOF) controller for interval type-2 (IT2) T–S fuzzy systems with state delay. For nonlinear systems, the IT2 fuzzy model is an efficient modeling method which can better express uncertainties than the (type-1) fuzzy model. In addition, state delay is also a general factor that affects system performance. After analyzing the stability of the system, based on convex linearization and the projection theorem, this article proposes a delay-dependent output-feedback controller design method. The IT2 membership functions (MFs) of the fuzzy controller are chosen to be different from those of the model so as to increase the freedom of controller selection. A membership-function-dependent (MFD) method based on the staircase MFs is applied to relax the stability analysis results. Finally, a numerical simulation example is given to illustrate the effectiveness of the results.