  Observer design for linear systems with aperiodic sampled-data measurements
is addressed. To solve this problem, a novel hybrid observer is designed. The
main peculiarity of the proposed observer consists of the use two output
injection terms, one acting at the sampling instants and one providing an
intersample injection. The error dynamics are augmented with a timer variable
triggering the arrival of a new measurement and analyzed via hybrid system
tools. Using Lyapunov theory, sufficient conditions for the convergence of the
observer are provided. Relying on those conditions, an optimal LMI-based design
is proposed for the observer gains. The effectiveness of the approach is
illustrated in an example.
