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Zbl 1113.93308
Gao, Huijun; Wang, Zidong; Wang, Changhong
Improved $\Cal H_{\infty}$ control of discrete-time fuzzy systems: a cone complementarity linearization approach.
(English)
[J] Inf. Sci. 175, No. 1-2, 57-77 (2005). ISSN 0020-0255

Summary: New results are presented for $\Cal H_{\infty}$ analysis and synthesis problems of discrete-time Takagi-Sugeno (TS) fuzzy systems. By defining a multiple Lyapunov function, a new sufficient condition guaranteeing the $\Cal H_{\infty}$ performance of the TS fuzzy systems is first derived, which is expressed by a set of linear matrix inequalities (LMIs). Both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework. Based on this new condition for $\Cal H_{\infty}$ performance, the corresponding $\Cal H_{\infty}$ controller design problem is then investigated. Different from thetraditional quadratic framework, the synthesis problem is solved by exploiting the cone complementarity linearization (CCL) method, together with a sequential minimization problem subject to LMI constraints obtained for the existence of admissible controllers, which can be readily solved by using standard numerical software.
MSC 2000:
*93B36 $H^\infty$-control
93C42 Fuzzy control

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