By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This publication develops a collection of reference equipment in a position to modeling uncertainties latest in club features, and examining and synthesizing the period type-2 fuzzy structures with wanted performances. It additionally presents various simulation effects for varied examples, which fill convinced gaps during this zone of analysis and will function benchmark recommendations for the readers.
Interval type-2 T-S fuzzy versions supply a handy and versatile technique for research and synthesis of complicated nonlinear platforms with uncertainties.
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Extra resources for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
18 1 Introduction Chapter 5 investigates the problem of output tracking control for IT2 fuzzy systems with actuator fault. An IT2 state-feedback fuzzy controller is designed to perform the tracking control problem, where the membership functions can be freely chosen since the number of fuzzy rules is different from that of the IT2 T–S fuzzy model. Based on Lyapunov stability theory, an existence condition of IT2 fuzzy H∞ output tracking controller is obtained to guarantee that the output of the closed-loop system can track the output of a given reference model well in the H∞ sense.
4) that the actual grades of membership, w˜ i (x(t)), can be reconstructed and expressed as a linear combination of wi (x(t)) and wi (x(t)), characterized by the LMFs and UMFs μ M˜ i ( f α (x(t))) and μ M˜ αi ( f α (x(t))), which are α scaled by the nonlinear functions αi (x(t)) and αi (x(t)), respectively. In other words, any membership functions within the FOU  can be reconstructed by the LMFs and UMFs. As the nonlinear plant is subject to parameter uncertainties, w˜ i (x(t)) will depend on the parameter uncertainties and thus leads to the values of αi (x(t)) and αi (x(t)) uncertain.
10) can be seen. The membership functions h˜ i j are reconstructed by the linear combination of the local LMFs and UMFs h i jl and h i jl . 21), the stability of the IT2 FMB control system is determined by the local LMFs and UMFs h i jl and h i jl . in kl . 23) to facilitate the stability analysis. 23). 7. 2, x > 0 and Q i j < 0 for all i and j can be achieved. 15) can be satisfied. in kl Wi jl −ε1 I < 0 for all i 1 , i 2 , . . , i n , k and l, which will be satisfied by a sufficiently small value of ε2 .