E. Maherzi1, M. Besbes*1, S. Zemmel2 and A. Mami3
1 High School of Technology and Computer Science, University of Carthage. 45 rue des entrepreneurs, Charguia 2, Tunis Carthage 2035, Tunisia. *mongi.besbes@gmail.com
2 High School of Applied Sciences and Technologies of Gafsa, University of Gafsa.
3 Department of physics, Faculty of Sciences of Tunis, University of El Manar.
ABSTRACT
]]> This paper treats the estimation of the state of a nonlinear system with unknown input. The nonlinear system is described by a multimodel with unknown function of activation but depending only on the state. The method of design of the multiobserver is described by using the second method of Lyapunov and their candidate functions. The sufficient obtained stability conditions are expressed in terms of Linear Matrix Inequalities (LMI) and are obtained first using the Lyapunov quadratic functions and secondly by using Lyapunov polyquadratic functions. This latter technique seems to be less conservative and less constraining than the first. Illustrative examples are presented in this paper.Keywords: Discrete multimodel; multiobserver with unknown inputs; non measurable variables of decision; quadratic stabilization; polyquadratic stabilization; unknown input estimation; Linear Matrix Inequalities (LMI).
RESUMEN
Este artículo trata la estimación de estado de un sistema no lineal con una entrada desconocida. El sistema no lineal se describe por un multi-modelo con una función desconocida de activación, pero dependiendo sólo en su estado. El método de diseño del multi-observador se detalla mediante el segundo método de Lyapunov y sus funciones candidatos. Las condiciones de estabilidad obtenidos se expresan en términos de desigualdades matriciales lineales (LMI) y se obtienen de la utilización de las funciones cuadráticas de Lyapunov en un primer estudio y de las funciones poli cuadráticas de Lyapunov en un segundo estudio que aparece menos conservador y menos restrictivo que el primero. Múltiples ejemplos ilustrativos se presentan en este documento.
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