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Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework.

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Title: Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework.
Authors: Wu, Ligang, Su, Xiaojie, Shi, Peng, Qiu, Jianbin
Source: IEEE Transactions on Fuzzy Systems; 04/01/2011, Vol. 19 Issue 2, p366-378, 13p
Subject Terms: DISCRETE-time systems, TIME delay systems, FUZZY systems, APPROXIMATION theory, NUMERICAL analysis, NONLINEAR systems, SYMMETRIC matrices, MATRIX inequalities
Abstract: This paper is concerned with the problem of H\infty 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\infty 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\infty error performance for the error system. Then, the H\infty 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\infty 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. [ABSTRACT FROM AUTHOR]
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Database: Complementary Index
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Abstract:This paper is concerned with the problem of H\infty 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\infty 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\infty error performance for the error system. Then, the H\infty 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\infty 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. [ABSTRACT FROM AUTHOR]
ISSN:10636706
DOI:10.1109/TFUZZ.2011.2104363