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

ISBN-10: 9811005923

ISBN-13: 9789811005923

ISBN-10: 9811005931

ISBN-13: 9789811005930

This publication develops a suite of reference equipment in a position to modeling uncertainties current in club services, and interpreting and synthesizing the period type-2 fuzzy platforms with wanted performances. It additionally presents various simulation effects for numerous examples, which fill sure gaps during this region of study and will function benchmark suggestions for the readers.

Interval type-2 T-S fuzzy types offer a handy and versatile approach for research and synthesis of advanced nonlinear platforms with uncertainties.

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

**Example text**

However, the IT2 FMB control systems can be imperfectly matched membership functions, potentially leading to more difficult stability analysis as the favorable property of PDC design concept vanishes. To carry out the stability analysis for IT2 FMB control system subject to imperfect premise membership functions, the LMFs and UMFs characterized the footprint of uncertainty (FOU) are chosen to be a favorable representation. This favorable representation allows the LMFs and UMFs to be taken in the stability analysis.

1 Introduction This chapter investigates the stability of IT2 FMB control systems under imperfect premise matching. Unlike the authors’ work in [97] under PDC design concept, it was required that the IT2 fuzzy controller shares the same premise membership functions and the same number of rules as those of the IT2 T–S fuzzy model. These limitations constrain the design flexibility and increase the implementation complexity of the IT2 fuzzy controller. This result of this chapter eliminates these limitations by proposing an IT2 fuzzy controller that the membership functions and the number of rules can be freely chosen enhancing the applicability of the IT2 FMB control scheme.

C, are matrices to be determined. 18) i=1 j=1 l=1 where Q i j = Ai X + X AiT + Bi N j + N jT BiT . 20) i=1 j=1 where M = M T ∈ Rn×n ia an arbitrary matrix and 0 ≤ Wi jl = WiTjl ∈ Rn×n . 20), we have p τ +1 c V˙ (t) = ξi jl γ i jl h i jl + γ i jl h i jl z T (t)Q i j z(t) i=1 j=1 l=1 p τ +1 c ξi jl γ i jl h i jl + (1 − γ i jl )h i jl z T (t)Q i j z(t) ≤ i=1 j=1 l=1 p τ +1 c ξi jl (1 − γ i jl ) h i jl − h i jl z T (t)Wi jl z(t) − i=1 j=1 l=1 ⎡ p c +⎣ τ +1 ⎤ ξi jl γ i jl h i jl + (1 − γ i jl )h i jl − 1⎦ z T (t)M z(t) i=1 j=1 l=1 ⎡ p = z T (t) ⎣ c τ +1 ⎤ ξi jl h i jl Q i j − h i jl − h i jl Wi jl + h i jl M − M ⎦ z(t) i=1 j=1 l=1 p c τ +1 + ξi jl γ i jl h i jl − h i jl z T (t) Q i j + Wi jl + M z(t).

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

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