French Champagne and Belgian Chocolate Problems in Simultaneous Stabilization of Linear Systems

摘要

This paper considers two open problems associated with simultaneous stabilization of linear systems, namely French champagne problem and Belgian chocolate problem. Based on the recent development in automated inequality-type theorem proving, the explicit bounds which guarantee the existence of stabilizing controllers with fixed order are determined. In addition, two conjectures concerning the Belgian chocolate problem are formulated. Some numerical examples are worked out.