Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based by Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao

  • admin
  • March 23, 2017
  • System Theory
  • Comments Off on Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based by Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao

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 features, and reading and synthesizing the period type-2 fuzzy structures with wanted performances. It additionally presents quite a few simulation effects for numerous examples, which fill convinced gaps during this zone of analysis and should function benchmark ideas for the readers.
Interval type-2 T-S fuzzy versions offer a handy and versatile process for research and synthesis of advanced nonlinear structures with uncertainties.

Show description

Read Online or Download Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems PDF

Best system theory books

Adaptive networks: theory, models and applications

With adaptive, advanced networks, the evolution of the community topology and the dynamical strategies at the community are both very important and infrequently essentially entangled. fresh learn has proven that such networks can show a plethora of recent phenomena that are eventually required to explain many real-world networks.

Modeling and Identification of Linear Parameter-Varying Systems

Throughout the prior twenty years, the framework of Linear Parameter-Varying (LPV) platforms has turn into a promising procedure theoretical method of h- dle the controlof mildly nonlinear and particularly place based platforms that are universal in mechatronic functions and within the approach ind- try out. The beginning of the program category used to be initiated via the necessity of engineers to accomplish greater functionality for nonlinear and time-varying dynamics, c- mon in lots of business functions, than what the classical framework of Linear Time-Invariant (LTI) keep watch over offers.

Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

Usual differential equations play a relevant position in technological know-how and feature been prolonged to evolution equations in Banach areas. for lots of purposes, notwithstanding, it really is tough to specify an appropriate normed vector area. Shapes with out a priori regulations, for instance, should not have an visible linear constitution.

Extra resources for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems

Sample text

5) where η j (x(t)) denotes the lower grades of membership and η j (x(t)) denotes the upper grades of membership, μM (gs (x(t))) stands for the LMF and μMjs (gs (x(t))) js stands for the UMF. μMjs (gs (x(t))) ≥ μM (gs (x(t))) ≥ 0 and η j (x(t)) ≥ η j (x(t)) ≥ 0 js for all j. 6) j=1 where ηj (x(t)) = ν j (x(t))η j (x(t)) + ν j (x(t))η j (x(t)) r l=1 ν l (x(t))η l (x(t)) + ν l (x(t))η l (x(t)) ≥ 0, ∀j, with r ηj (x(t)) = 1, j=1 0 ≤ ν j (x(t)) ≤ 1, ∀j, 0 ≤ ν j (x(t)) ≤ 1, ∀j, ν j (x(t)) + ν j (x(t)) = 1, ∀j, in which ν j (x(t)) and ν j (x(t)) are predefined functions, and ηj (x(t)) stands for the grades of membership of the embedded membership functions.

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. 1. 23) that V˙ (t) ≤ zT (t)Ψ1 z(t) − c |ξ(t)|2 . 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, the LMFs and UMFs are defined as follows: q 2 2 h i jl (x(t)) = n ... 9) n ... in kl are constant scalars to be determined; 0 ≤ vris kl (xr (t)) ≤ 1 and vr 1kl (xr (t)) + vr 2kl (xr (t)) = 1 for r, s = 1, 2, . . , n; l = 1, 2, . . , τ + 1; q ir = 1, 2; x(t) ∈ Φk ; otherwise, vris k (xr (t)) = 0. As a result, we have k=1 i21 =1 2 2 n i 2 =1 . . i n =1 r =1 vrir kl (xr (t)) = 1 for all l, which is used in the stability analysis. 11) l=1 with p c h˜ i j (x(t)) = 1. 12) i=1 j=1 In addition, 0 ≤ γ i jl (x(t)) ≤ γ i jl (x(t)) ≤ 1 are two functions, which are not necessary to be known, exhibiting the property that γ i jl (x(t)) + γ i jl (x(t)) = 1 for all i, j, l; ξi jl (x(t)) = 1 if the membership function h i jl (x(t)) is within the subFOU l, otherwise, ξi jl (x(t)) = 0.

Download PDF sample

Rated 5.00 of 5 – based on 6 votes