Strong, simultaneous, and reliable stabilization of finite-dimensional linear time-varying plants

Some issues related to the stabilization of linear, time-varying (LTV) plants are studied. The authors consider the class of finite-dimensional LTV plants that are internally stabilizable by output feedback, and show that every plant in the class can be stabilized by a stable LTV controller; moreover, they give a parameterization of all nonlinear time-varying controllers that stabilize a given LTV plant. Using these results, they show that every finite collection of LTV plants can be simultaneously stabilized by a stable LTV. Finally, the authors 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