Continuous-discrete observers for global stabilization of nonlinear systems with applications to bioreactors

In this paper nonlinear continuous time systems for which only some states are available in discrete time are considered. For a class of nonlinear systems, a simple continuous-discrete observer is given. The convergence rate is exponential but cannot be freely assigned. Under some conditions, it is shown that if there exists a globally exponentially state stabilizing feedback, if there exists an exponential continuous-discrete observer, then this feedback computed with the estimated states still stabilizes globally exponentially the system. An extension is done when the measurements are available with some lag. These results are applied to bioreactors.