Lyapunov theory for 2-D nonlinear Roesser models: application to asymptotic and exponential stability

Nima Yeganefar (1, 2) , Nader Yeganefar (3) , Mariem Ghamgui (1, 2) , Emmanuel Moulay (4)

1 LIAS [Poitiers] - Laboratoire d'informatique et d'automatique pour les systèmes [EA 6315]
2 A&S - Automatique et Systèmes
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités
4 XLIM-SIC - SIC

This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability.

Mots clés: $n{rm D}$ systems; Converse Lyapunov theorem; Lyapunov functions; nonlinear discrete systems

Domaines: Automatique / Robotique

Nima Yeganefar, Nader Yeganefar, Mariem Ghamgui, Emmanuel Moulay. Lyapunov theory for 2-D nonlinear Roesser models: application to asymptotic and exponential stability. IEEE Transactions on Automatic Control, 2013, 58 (5), pp.1299-1304. ⟨10.1109/TAC.2012.2220012⟩. ⟨hal-00862935⟩