Model Reduction of Takagi-Sugeno Fuzzy Stochastic Systems

• Published in: IEEE transactions on systems, man and cybernetics. Part B, Cybernetics Vol. 42; no. 6; pp. 1574 - 1585
• Main Authors: Xiaojie Su, Ligang Wu, Peng Shi, Yong-Duan Song
• Format: Journal Article
• Language: English
• Published: IEEE 01.12.2012
• Subjects: Cone complementary linearization; Fuzzy systems; Reduced order systems; Stochastic systems; Symmetric matrices; Takagi-Sugeno (T-S) fuzzy systems; Takagi-Sugeno model; {\cal H}_{\infty} model reduction
• ISSN: 1083-4419; 1941-0492
• DOI: 10.1109/TSMCB.2012.2195723

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.