Simultaneous Strong Stabilization of Linear Time-Varying Systems Using Switched Controllers

Abstract

The problem of simultaneously stabilizing a finite collection of linear time-invariant plants with a single controller is a problem that has attracted considerable interest (e.g., see [21]). In particular, if one restricts attention to the case of linear time-invariant controllers, the problem of finding a useful necessary and sufficient condition for simultaneous stabilization has remained unsolved. The motivation for the simultaneous stabilization problem is derived from the fact that many problems of robust control with parameter uncertainty can be approximated by a simultaneous stabilization problem. Also, the fact that the simultaneous stabilization problem is tantalizingly simple to state and yet apparently very difficult to solve has attracted many researchers.