H∞ state-feedback control for fuzzy systems with input saturation via fuzzy weighting-dependent Lyapunov functions

Authors:
Sung Hyun Kim;Chang Hee Lee;PooGyeon Park
Affiliations:
Electrical and Computer Engineering Division, Pohang University of Science and Technology, Pohang, Kyungbuk, 790-784, Republic of Korea;Electrical and Computer Engineering Division, Pohang University of Science and Technology, Pohang, Kyungbuk, 790-784, Republic of Korea;Electrical and Computer Engineering Division, Pohang University of Science and Technology, Pohang, Kyungbuk, 790-784, Republic of Korea
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

This paper proposes a method for designing an H"~ state-feedback fuzzy controller for discrete-time Takagi-Sugeno (T-S) fuzzy systems with input saturation. To address the input saturation problem, this paper first formulates a set invariance condition for the T-S fuzzy systems. Then, based on the set invariance condition, this paper establishes H"~ stabilization conditions associated with a fuzzy weighting-dependent Lyapunov function, where the fuzzy controller is designed to be dependent on not only the current-time but also the one-step-past information on the time-varying fuzzy weighting functions. In the derivation, the H"~ stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs), and then reconverted into LMIs by an efficient relaxation technique.