Stabilization of Linear Time-Varying Systems Strong, Simultaneous and Reliable Stabilization

In this paper we study some issues related to the stabilization of linear, time-varying (LTV) plants. We consider the class of finite-dimensional LTV plants and show that every plant that can be internally stabilized by output feedback can be stabilized by a stable LTV controller. We give a parametrization of all nonlinear time-varying controllers that stabilize a given LTV plant, and further, we show that every finite collection of LTV plants can be simultaneously stabilized by a stable LTV controller. Finally, we prove that every LTV plant can always be stabilized by a pair of simultaneously acting LTV controllers each reliable against a failure of the other.