Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 19, Issue 2, Pages 366-378Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2011.2104363
Keywords
Delay partitioning; discrete-time systems; H-infinity model approximation; Takagi-Sugeno (T-S) fuzzy systems; time delay
Funding
- National Natural Science Foundation of China [60804002]
- Natural Science Foundation of Heilongjiang Province of China [QC2009C58]
- Program for New Century Excellent Talents in University
- Chinese National Postdoctoral Science Foundation [20090460892]
- Special Chinese National Postdoctoral Science Foundation [201003449]
- Engineering and Physical Sciences Research Council, U.K. [EP/F029195]
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This paper is concerned with the problem of H-infinity 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-infinity 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-infinity error performance for the error system. Then, the H-infinity 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-infinity 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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