Non-quadratic stabilization of second order continuous Takagi-Sugeno descriptor systems via line-integral Lyapunov function

Marquez, Raymundo; Guerra, Thierry Marie; Kruszewski, Alexandre; Bernal, Miguel

doi:10.1109/fuzz-ieee.2014.6891868

Cited by 5 publications

(1 citation statement)

References 27 publications

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“…This was the idea behind a preliminary result presented in [21], introducing a larger class of path-independent lineintegral Lyapunov functions whenever the MFs depended on an arbitrary set of linear functions of the system states. Other refinements on the work of [13] can be found in [23,24]; they exploit a relaxation from a determinant formula which applies only to second-order TS systems, but do not correspond to the point of view hereby adopted (pursuing results applicable to higher-order systems).…”

Section: Introductionmentioning

confidence: 99%

A generalised integral polynomial Lyapunov function for nonlinear systems

González

Sala

Bernal

2019

Fuzzy Sets and Systems

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This work generalises the line-integral Lyapunov function in (Rhee & 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.

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Section: Introductionmentioning

confidence: 99%