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{cal H}_{\infty } Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems

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4 Author(s)
Xiaojie Su ; Space Control & Inertial Technol. Res. Center, Harbin Inst. of Technol., Harbin, China ; Ligang Wu ; Peng Shi ; Yong-Duan Song

This paper is concerned with the problem of H model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

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Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on  (Volume:42 ,  Issue: 6 )