Stabilization of linear time-varying descriptor systems by output feedback

This paper considers stabilization of linear time-varying descriptor systems by dynamic output feedback. We first introduce a necessary and sufficient condition for stability, which is expressed as solvability of linear matrix differential inequalities. Then, we consider a dynamic output feedback controller and apply the stability condition to the closed-loop system in order to derive a necessary and sufficient condition for stabilizability. The condition is expressed also in terms of linear matrix differential inequalities and a stabilizing controller can be computed by using the solution of the inequalities. Finally, we present a numerical example.