By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This ebook develops a suite of reference equipment in a position to modeling uncertainties present in club features, and examining and synthesizing the period type-2 fuzzy platforms with wanted performances. It additionally presents quite a few simulation effects for varied examples, which fill convinced gaps during this region of study and should function benchmark suggestions 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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Extra info for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
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, . . , r, G ∗ G3 appropriate dimensions, and under the condition k − σ¯ k θk ≥ 0 (0 < σ¯ k < 1) for all k = 1, 2, .
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 . 7 but not on the other way round. 4 Simulation Results 33 Fig. 1 An inverted pendulum system. c  IEEE. Reprinted, with permission, from ref. 9 In this example, we consider an inverted pendulum as shown in Fig. 1 subject to parameter uncertainties  as the nonlinear plant to be controlled.
Firstly, the state-feedback and the output-feedback control systems are constructed. A new performance index, referred to extended dissipativity performance, is introduced. The extended dissipativity is a generalization of the H∞ performance, the L2 -L∞ performance, the passivity performance and dissipativity performance. Secondly, based on Lyapunov stability theory, the state and output-feedback controllers are designed respectively to guarantee that the closed-loop system is asymptotically stable with extended dissipativity performance.
Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems by Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao