By Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao
This publication develops a suite of reference tools able to modeling uncertainties current in club capabilities, and interpreting and synthesizing the period type-2 fuzzy platforms with wanted performances. It additionally presents a number of simulation effects for numerous examples, which fill convinced gaps during this zone of study and should function benchmark ideas for the readers.
Interval type-2 T-S fuzzy versions offer a handy and versatile strategy for research and synthesis of complicated nonlinear structures with uncertainties.
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Additional resources for Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems
I = 1, 2, . . , p; Ψ is a positive integer; x (t) ∈ Rn is the system state vector; Ai ∈ Rn×n and Bi ∈ Rn×m are the known system and input matrices, respectively; u(t) ∈ Rm is the input vector. The firing strength of the ith rule is of the following interval sets: Wi (x (t)) = wi (x (t)) wi (x (t)) , i = 1, 2, . . , p, where Ψ wi (x (t)) = α=1 μ M˜ i ( f α (x (t))) ≥ 0, α Ψ wi (x (t)) = α=1 μ M˜ αi ( f α (x (t))) ≥ 0, μ M˜ αi ( f α (x (t))) ≥ μ M˜ i ( f α (x (t))) ≥ 0, α wi (x (t)) ≥ wi (x (t)) ≥ 0, ∀i, in which wi (x (t)), wi (x (t)), μ M˜ i ( f α (x (t))) and μ M˜ αi ( f α (x (t))) denote the lower α grade of membership, upper grade of membership, LMF and UMF, respectively.
I=1 j=1 This completes the proof. 8 () Given any matrices X , Y and Z > 0 with appropriate dimensions, then the inequality X T Y + Y T X ≤ X T Z X + Y T Z −1 Y holds. 3 Publication Contribution This book represents the some attempts to reflect the state-of-the-art of the research area for handling stability/performance analysis and optimal synthesis problems for IT2 T–S fuzzy systems. The content of this book can be divided into two parts. 14 1 Introduction The first part will provide analysis and synthesis of continuous-time IT2 T–S fuzzy systems.
12) is well defined. The second item enables one to derive LMI based condition for the investigation of the dissipativity analysis problem. 1 similar to (1), (2) and (5) were used in [52, 116]. On the other hand, when considering the L2 -L∞ performance, it is well known that the output of the considered system should not include disturbance inputs . 1. 1 is technically necessary for the development of our analysis and design methods. 12). 3 Main Results This section is concerned with the controllers design problem for IT2 T–S fuzzy system.
Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems by Hongyi Li, Ligang Wu, Hak-Keung Lam, Yabin Gao