By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This booklet develops a suite of reference equipment in a position to modeling uncertainties current in club capabilities, and reading and synthesizing the period type-2 fuzzy platforms with wanted performances. It additionally offers a variety of simulation effects for numerous examples, which fill sure gaps during this quarter of analysis and will function benchmark recommendations for the readers.
Interval type-2 T-S fuzzy types supply a handy and versatile procedure for research and synthesis of complicated nonlinear structures with uncertainties.
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Additional info for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
A novel type of IT2 switched output-feedback controller is designed to ensure that the closed-loop system is asymptotically stable with an H∞ performance. Chapter 7 investigates the problem of filter design for IT2 fuzzy systems with D stability constraints based on a new performance index. Attention is focused on solving the H∞ , L 2 -L ∞ , passive and dissipativity fuzzy filter design problems for IT2 fuzzy systems with D stability constraints in a unified frame. Under the new performance index frame, using Lyapunov stability theory, a novel type of IT2 filter is designed such that the filtering error system guarantees the prescribed H∞ , L 2 -L ∞ , passive and dissipativity performance levels with D stability constraints.
P; p is the number of premise variables; Kj ∈ Rm×n is the state-feedback gain matrix of rule j. 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.
10). in kl , which are brought to the stability conditions. 9), the cross terms, rn=1 vrir kl (xr (t)), are independent of i and j thus can be collected in the stability analysis. 11) as a linear combination of h i jl (x(t)) and h i jl (x(t)). in kl through n r =1 vrir kl (xr (t)). in kl . These properties can be seen in the stability analysis carried out in the next section. 7) is investigated based on the Lyapunov stability theory with the consideration of the information of the LMFs and UMFs, and sub-FOUs.