Observer based ℌ∞ controllers for a class of nonlinear lipschitz discrete-time systems

This paper deals with the problem of observer-based H∞ stabilization for a class of nonlinear discrete-time systems. We propose a new design strategy in order to compute simultaneously the observer and the controller parameters. Thanks to the use of some matrix decompositions and other mathematical artifacts, we provide a novel sufficient synthesis condition expressed in term of Linear Matrix Inequality (LMI). The effectiveness of the proposed method is shown through many numerical examples.