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LMI relaxations for nonquadratic stabilization of discrete-time Takagi-Sugeno systems based on polynomial fuzzy Lyapunov functions

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3 Author(s)
Eduardo S. Tognetti ; School of Electrical and Computer Engineering, University of Campinas - UNICAMP, CP 6101, 13083-970, SP, Brazil ; Ricardo C. L. F. Oliveira ; Pedro L. D. Peres

The problem of state-feedback control design for discrete-time Takagi-Sugeno fuzzy systems is investigated in this paper. The strategy relies on the use of a quadratic in the state Lyapunov function that presents a homogeneous polynomial dependence of arbitrary degree g on the first instant of time of the premise variables and a multi-affine dependence on the successive instants of time of the premise variables until a maximum instant of time M. The tests cast in the form of LMI relaxations parametrized on both g and M and a feasible solution yields a non-PDC controller based on homogeneous polynomial matrices. Numerical examples show that the approach can be less conservative and more efficient than other methods available in the literature.

Published in:

Control and Automation, 2009. MED '09. 17th Mediterranean Conference on

Date of Conference:

24-26 June 2009