Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
Kybernetika, Tome 46 (2010) no. 1, pp. 19-37.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions $V_n$ in a rational functional form approximating a maximal Lyapunov function $V_M$ that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions $V_n$ for a class of hybrid (piecewise non-linear) systems, where the dynamics is continuous on the boundary of the different regimes in the state space. In addition, a computationally feasible method is proposed to estimate the DOA using a maximal fitting hypersphere.
Classification : 34A34, 34A38, 34D20, 34D23, 34D35, 37B25, 70K20, 93D20
Keywords: maximal Lyapunov functions; domain of attraction; hybrid systems
@article{KYB_2010__46_1_a1,
     author = {Rozgonyi, Szabolcs and Hangos, Katalin M. and Szederk\'enyi, G\'abor},
     title = {Determining the domain of attraction of hybrid non{\textendash}linear systems using maximal {Lyapunov} functions},
     journal = {Kybernetika},
     pages = {19--37},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2010},
     mrnumber = {2666892},
     zbl = {1194.34018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_1_a1/}
}
TY  - JOUR
AU  - Rozgonyi, Szabolcs
AU  - Hangos, Katalin M.
AU  - Szederkényi, Gábor
TI  - Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
JO  - Kybernetika
PY  - 2010
SP  - 19
EP  - 37
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2010__46_1_a1/
LA  - en
ID  - KYB_2010__46_1_a1
ER  - 
%0 Journal Article
%A Rozgonyi, Szabolcs
%A Hangos, Katalin M.
%A Szederkényi, Gábor
%T Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
%J Kybernetika
%D 2010
%P 19-37
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2010__46_1_a1/
%G en
%F KYB_2010__46_1_a1
Rozgonyi, Szabolcs; Hangos, Katalin M.; Szederkényi, Gábor. Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions. Kybernetika, Tome 46 (2010) no. 1, pp. 19-37. http://geodesic.mathdoc.fr/item/KYB_2010__46_1_a1/