Continuous-discrete time observers for a class of MIMO nonlinear systems

In this paper, we investigate the possibility of designing an observer for a class of continuous-time dynamical systems with non-uniformly sampled measurements. More specifically, we propose an observer with a time varying gain witch converges exponentially under some conditions on the sampling partition diameter. The proposed observer is an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. As it is customarily done in the literature, we show that such an impulsive system can be split into two subsystems and be put under the form of a hybrid system which is designed using a continuous-time observer together with an inter-sample output predictor. Simulations results involving a typical bioreactor are given to show the effectiveness of the proposed observer.