Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based by Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao

By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao

This booklet develops a suite of reference tools able to modeling uncertainties latest in club services, and studying and synthesizing the period type-2 fuzzy structures with wanted performances. It additionally offers a number of simulation effects for numerous examples, which fill convinced gaps during this quarter of study and should function benchmark ideas for the readers.
Interval type-2 T-S fuzzy versions supply a handy and versatile approach for research and synthesis of complicated nonlinear platforms with uncertainties.

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I n , k, l: 32 2 Stabilization of Interval Type-2 Fuzzy-Model-Based Systems q 2 2 2 k=1 i 1 =1 i 2 =1 p n ... in kl M − M < 0. in kl M − M < 0. 7. 7) is guaranteed to be asymptotically stable. 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).

N; l = 1, 2, . . , τ + 1; q ir = 1, 2; x(t) ∈ Φk ; otherwise, vris k (xr (t)) = 0. As a result, we have k=1 i21 =1 2 2 n i 2 =1 . . i n =1 r =1 vrir kl (xr (t)) = 1 for all l, which is used in the stability analysis. 11) l=1 with p c h˜ i j (x(t)) = 1. 12) i=1 j=1 In addition, 0 ≤ γ i jl (x(t)) ≤ γ i jl (x(t)) ≤ 1 are two functions, which are not necessary to be known, exhibiting the property that γ i jl (x(t)) + γ i jl (x(t)) = 1 for all i, j, l; ξi jl (x(t)) = 1 if the membership function h i jl (x(t)) is within the subFOU l, otherwise, ξi jl (x(t)) = 0.

12) becomes the very-strict passivity performance. In the definition of the very-strict passivity performance, the scalar ρ is not required to be zero. It was shown in [134] that ρ should be a non-positive scalar. 1. 12), it follows that t ρ≤ eT (s)Ψ1 e(s)ds − eT (t)Φe(t). 1 that Φ ≥ 0 and Ψ1 ≤ 0. 2 Problem Formulation and Preliminaries 43 ˜ Ψ1 = −Ψ˜ 1T Ψ˜ 1 . 12) is well defined. The second item enables one to derive LMI based condition for the investigation of the dissipativity analysis problem.

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