Observer-based relaxed H∞ control for fuzzy systems using a multiple Lyapunov function

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

Citing 27
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Abstract

This short paper proposes a method of designing a fuzzy observer-based H∞ controller for discrete-timeTakagi-Sugeno (T-S) fuzzy systems. To enhance the applicability of the output-feedback controller and improve its performance, this short paper first builds a set of fuzzy control rules with premise variables different from those of the T-S fuzzy system, and sets the overall controller to be dependent on not only the current time but also the one-step-past information on the estimated fuzzy weighting functions. Then, based on the fuzzy control rules, this short paper establishes a less conservative H∞ stabilization condition incorporated with a multiple Lyapunov function dependent on the estimated fuzzy weighting functions. Through a two-step design procedure, the H∞ stabilization condition is formulated in terms of parameterized linear matrix equalities (PLMIs), which are reconverted into LMIs with the help of an efficient and effective relaxation scheme.