Relaxed H∞ stabilization conditions for discrete-time fuzzy systems with interval time-varying delays

Authors:
Sung Hyun Kim;PooGyeon Park
Affiliations:
Division of Electrical and Computer Engineering, Pohang University of Science and Technology, Pohang, Korea;Division of Electrical and Computer Engineering, Pohang University of Science and Technology, Pohang, Korea
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2009

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Abstract

To derive less-conservative delay-and range-dependentH∞ stabilization conditions for discrete-time Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays, the use of a fuzzy-weighting-dependent Lyapunov-Krasovskii functional (FWLKF), in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions, is proposed. Subsequently, parameterized linearmatrix inequality (PLMI)-based H∞ stabilization conditions are derived by following the free-weighting matrix approach. To fully exploit the convexity of fuzzy weighting functions, the derived PLMIs are sequentially replaced by a finite set of LMIs by considering all possible conditions associated with fuzzy weighting functions.