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{cal H}_{\infty } State-Feedback Control Design for Fuzzy Systems Using Lyapunov Functions With Quadratic Dependence on Fuzzy Weighting Functions

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2 Author(s)
Sung Hyun Kim ; Div. of Electr. & Comput. Eng., Pohang Univ. of Sci. & Technol., Pohang ; PooGyeon Park

This paper proposes a method for designing an Hinfin state-feedback fuzzy controller for discrete-time Takagi-Sugeno (T-S) fuzzy systems. To derive less conservative Hinfin stabilization conditions, this paper enhances the interactions among the fuzzy subsystems using a multiple Lyapunov function with quadratic dependence on fuzzy weighting functions. Besides, for more allocation of the nonlinearity to the fuzzy control system, this paper introduces a slack variable that is quadratically dependent on the one-step-past fuzzy weighting functions as well as the current ones. In the derivation, the Hinfin stabilization conditions are formulated in terms of parameterized linear matrix inequalities (PLMIs), which are reconverted into LMI conditions with the help of an efficient relaxation technique.

Published in:

Fuzzy Systems, IEEE Transactions on  (Volume:16 ,  Issue: 6 )

Date of Publication:

Dec. 2008

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