Time-Varying Simultaneous stabilization, Part I. Countable families of LTI systems

Abstract

In this paper, we introduce a new method that enables us to prove that given any finite family of LTI (linear time-invariant) systems, there exists a continuous time varying feedback law that simultaneously globally exponentially stabilizes this family. We then derive sufficient conditions for the simultaneous asymptotic stabilizability of countably infinite families of LTI systems. In both cases we provide simple design procedures as well as explicit controls.