By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This publication develops a collection of reference tools in a position to modeling uncertainties latest in club services, and interpreting and synthesizing the period type-2 fuzzy structures with wanted performances. It additionally presents a number of simulation effects for varied examples, which fill yes gaps during this quarter of study and should function benchmark ideas for the readers.
Interval type-2 T-S fuzzy versions offer a handy and versatile technique for research and synthesis of complicated nonlinear structures with uncertainties.
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Additional info for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
1, we have V˙ (t) ≤ −c |ξ(t)|2 . 7) with w(t) = 0 is asymptotically stable. This completes the proof. 3). 3, the following theorem is obtained directly. 1, if there exist matrices P = PT > 0, G > 0 and 48 3 Output-Feedback Control of Interval Type-2 Fuzzy-Model-Based Systems Λ˜ Ti = Λ˜ i (i = 1, 2, . . 34) where ⎡ ¯ 1i − C¯ iT Ψ2 He(PA¯ ik ) PD T ⎣ ¯ 2i Πik = ∗ −He(D Ψ2 ) − Ψ3 ∗ ∗ −G C¯ iT Φ˜ T Θ˜ 2 = . 9) will be solved. 1, if there exists matrices ¯ = G1 G2 > 0, R > 0, S > 0, Ai , Bi and Ci with Λ¯ Ti = Λ¯ i , i = 1, 2, .
P; j = 1, 2, . . , c; l = 1, 2, . . in kl M i=1 j=1 − M < 0, ∀i 1 , i 2 , . . in kl , i = 1, 2, . . , p; j = 1, 2, . . , c; i 1 , i 2 , . . , i n = 1, 2; k = 1, 2, . . , q; l = 1, 2, . . 9); Q i j = Ai X + X AiT + Bi N j + N jT BiT for all i and j; and the feedback gains are defined as G j = N j X −1 for all j. 10). 17) where 0 < P = P T ∈ Rn×n . The main objective is to develop a condition guaranteeing that V (t) > 0 and V˙ (t) < 0 for all x(t) = 0. According to the Lyapunov stability theorem, by satisfying V (t) > 0 and V˙ (t) < 0 for all x(t) = 0, the IT2 FMB control system is guaranteed to be asymptotically stable, implying that x(t) → 0 as t → ∞.
5 Conclusion The stability of IT2 FMB control systems subject to parameter uncertainties has been investigated. Under the imperfect premise matching, the IT2 fuzzy controller can choose freely the premise membership functions and the number of rules different from the IT2 T–S fuzzy model, enhancing the design flexibility and reducing the implementation complexity. To facilitate the stability analysis, a favorable form of LMFs and UMFs has been proposed and the information of sub-FOUs has been considered.