Extended Stabilizing Controllers for Continuous-Time Descriptor Systems
Résumé
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 found such that: -The closed-loop is admissible; - Only the internal stability of a part of the generalized closed-loop is sought. First, the necessary and sufficient conditions for the existence of a solution are explicitly given in terms of two structured generalized Sylvester equations. Moreover, the parametrization of a class of controllers satisfying such stability is formulated. Finally, numerical examples are presented to show the effectiveness of the proposed results.