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Type: Journal article
Title: Model approximation for discrete-time state-delay systems in the T-S fuzzy framework
Author: Wu, L.
Su, X.
Shi, P.
Qiu, J.
Citation: IEEE Transactions on Fuzzy Systems, 2011; 19(2):366-378
Publisher: IEEE-Inst Electrical Electronics Engineers Inc
Issue Date: 2011
ISSN: 1063-6706
Statement of
Ligang Wu, Xiaojie Su, Peng Shi, and Jianbin Qiu
Abstract: This paper is concerned with the problem of H∞ model approximation for discrete-time Takagi-Sugeno (T-S) fuzzy time-delay systems. For a given stable T- S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an H∞ performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an H∞ error performance for the error system. Then, the H∞ model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, H∞ model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.
Keywords: Delay partitioning
discrete-time systems
H∞ model approximation
Takagi–Sugeno (T–S) fuzzy systems
time delay.
Rights: © 2011 IEEE
DOI: 10.1109/TFUZZ.2011.2104363
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Electrical and Electronic Engineering publications

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