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

This ebook develops a collection of reference tools in a position to modeling uncertainties present in club services, and interpreting and synthesizing the period type-2 fuzzy platforms with wanted performances. It additionally presents various simulation effects for numerous examples, which fill convinced gaps during this quarter of study and should function benchmark strategies for the readers.

Interval type-2 T-S fuzzy types offer a handy and versatile process for research and synthesis of advanced nonlinear structures with uncertainties.

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**Extra resources for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems**

**Example text**

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. 2) serves as a mathematical tool to facilitate the stability analysis and control synthesis, and is not necessarily implemented. 2). Controller Form: j j Rule i: IF g1 (x(t)) is N˜ 1 and . . 5) j where N˜ β is an IT2 fuzzy set of rule j corresponding to the function gβ (x(t)), β = 1, 2, . . , Ω; j = 1, 2, . . , c; Ω is a positive integer; G j ∈ Rm×n , j = 1, 2, .

Plant Form: Rule i: IF f 1 (x(t)) is M˜ 1i and . . 1) where M˜ αi is an IT2 fuzzy set of rule i corresponding to the function f α (x (t)), α = 1, 2, . . , Ψ ; i = 1, 2, . . , p; Ψ is a positive integer; x (t) ∈ Rn is the system state vector; Ai ∈ Rn×n and Bi ∈ Rn×m are the known system and input matrices, respectively; u(t) ∈ Rm is the input vector. The firing strength of the ith rule is of the following interval sets: Wi (x (t)) = wi (x (t)) wi (x (t)) , i = 1, 2, . . , p, where Ψ wi (x (t)) = α=1 μ M˜ i ( f α (x (t))) ≥ 0, α Ψ wi (x (t)) = α=1 μ M˜ αi ( f α (x (t))) ≥ 0, μ M˜ αi ( f α (x (t))) ≥ μ M˜ i ( f α (x (t))) ≥ 0, α wi (x (t)) ≥ wi (x (t)) ≥ 0, ∀i, in which wi (x (t)), wi (x (t)), μ M˜ i ( f α (x (t))) and μ M˜ αi ( f α (x (t))) denote the lower α grade of membership, upper grade of membership, LMF and UMF, respectively.

12) reduces to the strict (Q, S, R)-dissipativity [116]. 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.