Extended stabilizing controllers for continuous-time descriptor systems

This paper investigates the so-called extended stabilization control problem for continuous-time descriptor systems. In such nonstandard stabilization problem, the generalized plant and its unstable and/or nonproper weights are all described within the descriptor framework. The extended stabilizing controller (ESC) is sought such that: -The closed-loop is admissible;- Only the internal stability of a part of the closed-loop is required. A necessary and sufficient condition for the existence of a solution is explicitly given in terms of two structured generalized Sylvester equations. Moreover, the parametrization of a class of controllers satisfying such stability is formulated.