A non-quadratic Lyapunov functional for H∞ control of nonlinear systems via Takagi–Sugeno models

Raymundo Márquez Borbόn (1, 2) , Thierry-Marie Guerra (1) , Miguel Bernal (2) , Alexandre Kruszewski (3)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
2 ITSON - Instituto Tecnológico de Sonora
3 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

This paper presents a novel non-quadratic Lyapunov functional with time delay for controller design and H∞ disturbance rejection for nonlinear systems. Based on an exact Takagi–Sugeno representation of the nonlinear model, a proper integral structure for Lyapunov-based design allows circumventing the well-known problem of handling the time derivatives of the membership functions without imposing additional requirements. The methodology proposed that both increase the complexity of the classical quadratic LMI design and the control law structure, but in a reasonable manner. The main advantages are that the conditions in the proposed approach are expressed as linear matrix inequalities and proven to outperform previous results on the same subject. Illustrative examples are included to point out the aforementioned contributions

Domaines: Automatique

Raymundo Márquez Borbόn, Thierry-Marie Guerra, Miguel Bernal, Alexandre Kruszewski. A non-quadratic Lyapunov functional for H∞ control of nonlinear systems via Takagi–Sugeno models. Journal of The Franklin Institute, 2016, 353 (4), pp.781 - 796. ⟨10.1016/j.jfranklin.2016.01.004⟩. ⟨hal-01410230⟩