By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This ebook develops a collection of reference equipment in a position to modeling uncertainties latest in club capabilities, and reading and synthesizing the period type-2 fuzzy platforms with wanted performances. It additionally presents a variety of simulation effects for varied examples, which fill sure gaps during this zone of study and will function benchmark ideas for the readers.
Interval type-2 T-S fuzzy versions supply a handy and versatile strategy for research and synthesis of advanced nonlinear structures with uncertainties.
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Additional info for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
8) where xˆ (t) ∈ Rn is the state vector of the dynamic output-feedback controller; Nks stands for the kth fuzzy set of the function hs (x(t)), k = 1, 2, . . , r, s = 1, 2, . . , p; p is the number of premise variables; Ack , Bck and Cck are control gain matrices with appropriate dimensions. The firing strength of the kth rule is the following interval set: p ˜ k (x(t)) = p μN (hs (x(t))) , = μNks (hs (x(t))) ks s=1 s=1 k (x(t)), k (x(t)) , where k (x(t)) denotes the lower grades of membership and k (x(t)) denotes the upper grades of membership, μN (hs (x(t))) stands for the LMF and μNks (hs (x(t))) ks stands for the UMF.
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, . . , c, are the constant feedback gains to be determined. The firing strength of the jth rule is the following interval sets: M j (x(t)) = m j (x(t)) m j (x(t)) , j = 1, 2, . . , c, 26 2 Stabilization of Interval Type-2 Fuzzy-Model-Based Systems where Ω m j (x(t)) = β=1 μ N˜ j (gβ (x(t))) ≥ 0, β Ω m j (x(t)) = μ N˜ j (gβ (x(t))) ≥ 0, β=1 β μ N˜ j (gβ (x(t))) ≥ μ N˜ j (gβ (x(t))) ≥ 0, ∀ j, β β in which m j (x(t)), m j (x(t)), μ N˜ j (gβ (x(t))) and μ N˜ j (gβ (x(t))) stand for the lower β β grade of membership, upper grade of membership, LMF and UMF, respectively.
We first construct an IT2 fuzzy state-feedback controller  for the following control design. 2 Problem Formulation and Preliminaries 39 state-feedback controller do not share the same membership functions. The jth rule of the fuzzy controller is of the following form: Controller Form: Rule i: IF g1 (x(t)) is Mj1 and . . 4) where Mjs stands for the jth fuzzy set of the function gs (x(t)), j = 1, 2, . . r, s = 1, 2, . . p; p is the number of premise variables; Kj ∈ Rm×n is the state-feedback gain matrix of rule j.
Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems by Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao