A hybrid observer with a continuous intersample injection in the presence of sporadic measurements

This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability of a set wherein the estimation error is equal to zero. Moreover, three computationally efficient procedures are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in two examples.