Model approximation for discrete-time state-delay systems in the T-S fuzzy framework

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Wu, Ligang, Su, Xiaojie, Shi, Peng and Qiu, Jianbin (2011) Model approximation for discrete-time state-delay systems in the T-S fuzzy framework. IEEE Transactions on Fuzzy Systems, 19 (2). pp. 366-378. ISSN 1063-6706

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.

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Item type Article
URI https://vuir.vu.edu.au/id/eprint/7136
DOI https://doi.org/10.1109/TFUZZ.2011.2104363
Official URL http://dx.doi.org/10.1109/TFUZZ.2011.2104363
Subjects Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
Current > FOR Classification > 0906 Electrical and Electronic Engineering
Historical > SEO Classification > 970108 Expanding Knowledge in the Information and Computing Sciences
Keywords ResPubID21746, delay partitioning, discrete-time systems, H∞ model approximation, Takagi–Sugeno (T–S) fuzzy systems, time delay
Citations in Scopus 268 - View on Scopus
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