Simultaneous stabilization of LTI systems by means of nonlinear time-varying feedback

The simultaneous stabilization of a countable family of control systems consists in finding a feedback law that asymptotically stabilizes all the systems in the family. 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 nonlinear time-varying feedback law which simultaneously globally exponentially stabilizes this family. We also 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 feedback laws