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Model Approximation for Discrete-Time State-Delay Systems in the T-S Fuzzy Framework
Ist Teil von
IEEE transactions on fuzzy systems, 2011-04, Vol.19 (2), p.366-378
Ort / Verlag
New York: IEEE
Erscheinungsjahr
2011
Quelle
IEEE Electronic Library Online
Beschreibungen/Notizen
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.