Robust State Observation for Sampled-Data Nonlinear Systems with Exact and Euler Approximate Models

An LMI approach is proposed for the design of
<sup>robust

H</sup>
infin
^observers
for a class of Lipschitz nonlinear systems. Two type of systems are considered, Lipschitz nonlinear discrete-time systems and Lipschitz nonlinear sampled-data systems with Euler approximate discrete-time models. Observer convergence when the exact discrete-time model of the system is available is shown. Then, practical convergence of the proposed observer is proved using the Euler approximate discrete-time model. As an additional feature, maximizing the admissible Lipschitz constant, the solution of the proposed LMI optimization problem guaranties robustness against some nonlinear uncertainty. The robust H
_infin
observer synthesis problem is solved for both cases. The maximum disturbance attenuation level is achieved through LMI optimization.