By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This ebook develops a suite of reference tools able to modeling uncertainties present in club features, and studying and synthesizing the period type-2 fuzzy structures with wanted performances. It additionally offers quite a few simulation effects for numerous examples, which fill definite gaps during this quarter of study and should function benchmark options for the readers.
Interval type-2 T-S fuzzy types supply a handy and versatile strategy for research and synthesis of advanced nonlinear platforms with uncertainties.
Read or Download Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems PDF
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Extra resources for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
P; p is the number of premise variables; x(t) ∈ Rn is the system state vector, u(t) ∈ Rm is the input vector, w(t) ∈ Rh denotes the disturbance input which belongs to L2 [0, ∞), z(t) ∈ Rq is the control output and y(t) ∈ Rg is the measure output; Ai , Bi , Ci , D1i , D2i and Cyi are the known matrices with appropriate dimensions. 2) where θi (x(t)) denotes the lower grades of membership and θ i (x(t)) denotes the upper grades of membership, μW (fs (x(t))) stands for the LMF and μWis (fs (x(t))) stands is for the UMF.
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 → ∞. Denote z(t) = X −1 x(t) and X = P −1 .
Firstly, we consider the case when Φ = 0. 26), for any t ≥ 0, t J(s)ds ≥ x T (t)Gx(t) + ρ ≥ ρ. 27) holds by noting that zT (t)Φz(t) ≡ 0. Secondly, we consider the case of Φ = 0. 1 that Ψ1 + Ψ2 = 0 and D2i = 0, which implies that Ψ1 = 0, Ψ2 = 0 and Ψ3 > 0. Thus, J(s) = w T (s)Ψ3 w T (s) ≥ 0. 16), it can be obtained that C˜ iT Φ C˜ i ≤ G. For any t ≥ 0, the following inequalities hold: t t J(s)ds − zT (t)Φz(t) ≥ 0 r r J(s)ds − 0 θi ηj i=1 j=1 × (Ci x(t) + D2i w(t))T Φ (Ci x(t) + D2i w(t)) t = r 0 θi ηj g T (t)C˜ iT Φ C˜ i g(t) i=1 j=1 t ≥ r J(s)ds − r r J(s)ds − 0 θi ηj x T (t)Gx(t) ≥ ρ.