Observers design for one-sided Lipschitz discrete-time systems

Mohamed Benallouch (1) , Mohamed Boutayeb (2) , Michel Zasadzinski (2)

1 Advanced Materials & Structures
2 CRAN - Centre de Recherche en Automatique de Nancy

This note focuses on state observer design for a general class of nonlinear discrete-time systems that satisfies the one-sided Lipschitz condition. It has been shown that this condition may encompass a large class of nonlinearities. However, challenging problems arise such as relevant choice of the Lyapunov function or non convexity of the obtained stability conditions. Both full-order and reduced-order observer design are considered. In this work, the main contribution is to provide first some mathematical artifacts on the Lyapunov function to obtain simple and workable stability conditions, furthermore we show how to obtain LMIs conditions to assure asymptotic convergence. On the other hand, we extend the obtained results to $n-p$ reduced order observer design. High performances are shown through simulation results.

Mots clés: One-sided Lipschitz condition; Quadratic inner-boundedness; Nonlinear observers; Discrete-time nonlinear systems; Linear matrix inequality (LMI) approach; Lyapunov stability

Domaines: Automatique / Robotique

Mohamed Benallouch, Mohamed Boutayeb, Michel Zasadzinski. Observers design for one-sided Lipschitz discrete-time systems. Systems and Control Letters, 2012, 61 (9), pp.879-886. ⟨10.1016/j.sysconle.2012.05.005⟩. ⟨hal-00751553⟩