By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao

This booklet develops a suite of reference tools in a position to modeling uncertainties present in club capabilities, and reading and synthesizing the period type-2 fuzzy platforms with wanted performances. It additionally presents a variety of simulation effects for varied examples, which fill convinced gaps during this region of analysis and will function benchmark ideas for the readers.
Interval type-2 T-S fuzzy versions offer a handy and versatile procedure for research and synthesis of advanced nonlinear structures with uncertainties.

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I=1 j=1 Therefore, there is always a sufficiently small scalar c > 0 such that Ω˜ ij ≤ −cI. This means that V˙ (x(t)) − J(t) ≤ −c |ξ(t)|2 . 23) Thus J(t) ≥ V˙ (t) holds for any t ≥ 0, which means t J(s)ds ≥ V (x(t)) − V (x(0)). 24) 0 It is shown from (G − I) G−1 (G − I) ≥ 0 with G > 0 that − G−1 ≤ G − 2I. 25), we know that P > G, which means V (x(t)) = x T (t)Px(t) ≥ x T (t)Gx(t) ≥ 0. 20) that t J(s)ds ≥ x T (t)Gx(t) + ρ, ∀t ≥ 0. 1: t 0 J(t)dt − zT (t)Φz(t) ≥ ρ. 3 Main Results 47 To this end, we consider the two cases of Φ = 0 and Φ = 0, respectively.

C, are the constant feedback gains to be determined. The firing strength of the jth rule is the following interval sets: M j (x(t)) = m j (x(t)) m j (x(t)) , j = 1, 2, . . , c, 26 2 Stabilization of Interval Type-2 Fuzzy-Model-Based Systems where Ω m j (x(t)) = β=1 μ N˜ j (gβ (x(t))) ≥ 0, β Ω m j (x(t)) = μ N˜ j (gβ (x(t))) ≥ 0, β=1 β μ N˜ j (gβ (x(t))) ≥ μ N˜ j (gβ (x(t))) ≥ 0, ∀ j, β β in which m j (x(t)), m j (x(t)), μ N˜ j (gβ (x(t))) and μ N˜ j (gβ (x(t))) stand for the lower β β grade of membership, upper grade of membership, LMF and UMF, respectively.

4 Publication Outline The general layout of presentation of this monograph is divided into two parts. Part one focuses on the analysis and synthesis for continuous-time IT2 fuzzy systems, whilst second part studies the analysis and synthesis for discrete-time IT2 fuzzy systems. The organization structure of this monograph is shown in Fig. 4, and the main contents of this monograph are shown in Fig. 5. Chapter 1 presents the research background, motivations and research problems, which involve state-feedback control design, output-feedback control design, tracking control design, filter design, and fault detection design for of IT2 T– S fuzzy systems, and then the outline of the monograph is listed.

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