Sufficient LMI stability conditions for Lur'e type systems governed by a control law designed on their Euler approximate model
Résumé
In this paper, the stability issue of Lur'e systems governed by a control law stabilizing their forward Euler approximate model is investigated. More specifically the considered control law is obtained by exploiting the advantages of a new Lur'e type Lyapunov function with disconnected level sets. This Lyapunov function is adapted to the discrete-time Lur'e systems and to the structure of the forward Euler approximate model. The main result consists of LMI conditions allowing to guarantee that the continuous time Lur'e system associated with the proposed piecewise constant control law is globally asymptotically stable. The relevance of this approach is illustrated using a numerical example.