Multi-rate Sampled-data Observers Based on a Continuous-time Design

A multi-rate sampled-data observer for nonlinear systems under asynchronous sampling is developed in this work. The proposed multi-rate observer is based on a continuous-time design coupled with inter-sample predictors for the sampled measurements. The sampled-data system with the multi-rate observer forms a hybrid system and it is shown that the error dynamics of the overall system is input-to-output stable with respect to measurement errors, by applying the Karafyllis-Jiang vector small-gain theorem. This sampled-data design also offers robustness with respect to perturbations in the sampling schedule. A numerical example is given to show the effectiveness of the proposed method.