A Time-varying Observer for Linear Systems with Asynchronous Discrete-Time Measurements

In this paper we propose a time-varying observer for a linear continuous-time plant with asynchronous discrete-time measurements. The proposed observer is contextualized in the hybrid systems framework providing an elegant setting for the proposed solution. In particular some theoretical tools are provided, in terms of LMIs, certifying asymptotic stability of a certain compact set where the estimation error is zero. Moreover the case of asynchronous measurements is considered, i.e. when the measurements are not provided in well defined time instants, but they occur at an arbitrary time in a certain time interval. A design procedure based on the numerical solution of an infinite-dimensional LMI is also proposed, leading to a time-varying observer gain. Finally a numerical example shows the effectiveness of the proposed approach.