A new LMI based functional $H_\infty$ observer for Lipschitz discrete time systems
Résumé
The objective of this paper is to propose a functional $H_\infty$ observer for a general class of Lipschitz nonlinear discrete-time systems. The use of
reformulations of both the Lipschitz condition and the Young's inequality provide a new and less conservative LMI approach. This LMI deals with $H_\infty$ asymptotic stability of the estimation error in the presence of disturbances that affects the state of the system. Necessary and sufficient conditions for the existence of the unbiased functional observer are given. To demonstrate the effectiveness of the proposed filter, a numerical example is considered.