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Coutinho, Pedro H. S., Oliveira, Pedro M., Bessa, Iury, Lacerda, Marcio J. and Palhares, Reinaldo M. (2025) Data-driven nonquadratic stabilization of Takagi-Sugeno fuzzy systems. Journal of the Franklin Institute. ISSN 0016-0032
This work presents a new data-driven fuzzy control framework for the nonquadratic stabilization of Takagi-Sugeno (TS) fuzzy systems. We provide a data-driven stabilization condition via a nonquadratic Lyapunov function using only trajectory data collected from the system. Moreover, we propose a systematic methodology to obtain data-driven TS representations of nonlinear systems from a given dictionary of premise variables, via the sector nonlinearity approach. Besides synthesizing the fuzzy controller such that the origin of the closed-loop system is asymptotically stable, we provide an estimate of the region of attraction of the closed-loop equilibrium with formal guarantees. The estimate of the region of attraction is crucial to enable the implementation of the fuzzy controller in circumstances where the membership functions are well-defined for the state trajectory lying in a given region of validity. Numerical examples illustrate the effectiveness of the proposed data-driven fuzzy control
framework.
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