By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This e-book develops a suite of reference equipment able to modeling uncertainties latest in club services, and examining 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 zone of analysis and should function benchmark options for the readers.
Interval type-2 T-S fuzzy versions offer a handy and versatile procedure for research and synthesis of advanced nonlinear platforms with uncertainties.
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Extra info for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
12) is well defined. The second item enables one to derive LMI based condition for the investigation of the dissipativity analysis problem. 1 similar to (1), (2) and (5) were used in [52, 116]. On the other hand, when considering the L2 -L∞ performance, it is well known that the output of the considered system should not include disturbance inputs . 1. 1 is technically necessary for the development of our analysis and design methods. 12). 3 Main Results This section is concerned with the controllers design problem for IT2 T–S fuzzy system.
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). 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 .
The existence conditions of the controllers are given in the following theorems. We first present IT2 fuzzy state-feedback controller design results. 1, if there exist matrices G = GT > 0, Q = QT > 0, ΛTi = Λi , Mj (i, j = 1, 2, . . , r) with appropriate dimensions, and under the condition ηj − σj θj ≥ 0 (0 < σj < 1) for all j = 1, 2, . . 19) 44 3 Output-Feedback Control of Interval Type-2 Fuzzy-Model-Based Systems where ⎡ Ω¯ 11ij ⎣ Ωij = ∗ ∗ Ω¯ 12ij Ω¯ 22ij ∗ ⎤ Ω¯ 13ij Ω¯ 23ij ⎦ , −I −Q Q −G C˜ iT Φ˜ T , , Θ2ij = ∗ G − 2I ∗ −I C˜ i = Ci Q, Ω¯ 13ij = C˜ iT Ψ˜ 1T , Ω¯ 11ij = He(Ai Q + Bi Mj ), T T ˜T Ω¯ 12ij = D1i − C˜ iT Ψ2 , Ω¯ 22ij = −He(D2i Ψ1 .