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

• Published in: IEEE transactions on cybernetics Vol. 52; no. 6; pp. 4198 - 4208
• Main Authors: Zeng, Yi, Lam, Hak-Keung, Xiao, Bo, Wu, Ligang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control systems; Control systems design; Delay; Delays; Discrete-time system; Feedback control; Fuzzy control; Fuzzy systems; fuzzy-model-based (FMB) system; Mathematical models; Nonlinear systems; Numerical stability; Output feedback; output-feedback control; Power system stability; Stability analysis; Stability criteria; state-delay interval type-2 (IT2) fuzzy system; Uncertainty
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2020.3024754

This article investigates the design of the <inline-formula> <tex-math notation="LaTeX">\ell _{2}-\ell _{\infty } </tex-math></inline-formula> 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.