Section: New Results

Observers with discrete measurements

Participants : Frédéric Mazenc, Michael Malisoff [LSU] , Saeed Ahmed [University of Kaiserslautern, Germany] .

We studied the important case where the measurements of a system are discrete because output of this type may preclude the use of observers designed under the assumption that the measurements are continuous.

In the paper [25], we have studied time-varying linear systems in the difficult case where the inputs and outputs have sampling and delays, and where the systems and outputs contain uncertainties. The observers we have proposed are of continuous-discrete type and have no distributed terms. We allowed the delays to be arbitrarily large and proved that the observer in combination with a linear control result in an input-to-state stability, under delays and sampling. We illustrated our work in two examples including a DC motor model.

In the work [38], we have revisited a well-known contribution of observer design for continuous-time systems with discrete measurements which relies on a dynamic extension. Using a stability analysis which relies on the recent technique called "trajectory based approach", we proved that, for systems with asynchronous sampling, the proposed dynamic observer is converging even when the size of some (sufficiently scarce) intervals between 2 measurements is larger than the upper bound ensuring convergence of the observer that is provided in the literature. A scarcety condition on these intervals is exhibited.