  This paper deals with the problem of estimating the state of a linear
time-invariant system in the presence of sporadically available measurements
and external perturbations. 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 with a given decay rate to a set wherein the estimation
error is equal to zero. Robustness with respect to external perturbations and
$\mathcal{L}_2$-external stability from the plant perturbation to a given
performance output are considered. Moreover, computationally efficient
algorithms based on the solution to linear matrix inequalities are proposed to
design the observer. Finally, the effectiveness of the proposed methodology is
shown in three examples.
