A generalised integral polynomial Lyapunov function for nonlinear systems

Abstract

[EN] This work generalises the line-integral Lyapunov function in (Rhee and Won, 2006) for stability analysis of continuous-time nonlinear models expressed as fuzzy systems. The referred result applied only to Takagi¿Sugeno representations, and required memberships to be a tensor-product of functions of a single state; these are generalised here so that membership arguments can be arbitrary polynomials of the state variables; in this way, systems for which earlier results cannot be applied are now covered. Both the modelling and the integral terms appearing in the Lyapunov functions are generalised to a fuzzy polynomial case. Illustrative examples show the advantage of the proposed method against previous literature, even in the TS case.The authors gratefully to the financial support of Spanish ministry of Economy and European Union, grant DPI2016-81002-R (AEI/FEDER, UE), the CONACyT/COECyT Sonora scholarship 383252, and Project ITSON-PROFAPI-CA 2017-0088.Gonzalez-German, IT.; Sala, A.; Bernal Reza, MÁ. (2019). A generalised integral polynomial Lyapunov function for nonlinear systems. Fuzzy Sets and Systems. 356:77-91. https://doi.org/10.1016/j.fss.2018.02.005S779135