Some Open Problems on Simultaneous Stabilization of Linear Systems

Abstract

Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory, and is of theoretical and practical significance. In this paper, the authors review the recent research progress and the state-of-art results on simultaneous stabilization of single-input single-output linear time-invariant systems. Especially, the authors list the ever best results on the parameters involved in the well known “French Champagne Problem” and “Belgian Chocolate Problem” from the point of view of mathematical theoretical analysis and numerical calculation. And the authors observed that Boston claimed the lower bound of δ can be enlarged to 0.976461 in 2012 is not accurate. The authors hope it will inspire further study on simultaneous stabilization of several linear systems.