Impulsive observer-based control for linear systems using irregularly sampled measurements

In this paper, we consider the issue of stabilizing a class of linear systems using irregular sampled output measurements. For this purpose, we design a standard linear state feedback controller and an impulsive observer to provide an estimate the non-measured states, which are subsequently fed back in the control algorithm. We consider linear systems that can be decomposed, via a change of coordinates, into their respective measured and unmeasured dynamics. We consider the cases where the unmeasured subspace is stable and unstable respectively. In the case where the unmeasured subspace is stable, we employ a standard impulsive observer coupled with a continuous linear feedback control to stabilise the system. In the case where the unmeasured subspace is unstable, we employ two cascaded observers — an impulsive and a Luenberger observer — in conjunction with a linear feedback control to stabilise the latter. In order to prove the stability of the overall closed-loop system we proposed a practical stability result for a class of linear impulsive systems. Some simulation results are presented to show the performance of the observer-based control. Finally, some conclusions are drawn.