Uniform ensemble controllability for one-parameter families of time-invariant linear systems

In this paper we derive necessary as well as sufficient conditions for approximate controllability of parameter-dependent linear systems in the supremum norm. Using tools from complex approximation theory, we prove the existence of parameter-independent open-loop controls that steer the zero initial state of an ensemble of linear systems uniformly to a prescribed family of terminal states. New necessary conditions for uniform ensemble controllability of single-input systems are derived. Our results extend earlier ones of Li for ensemble controllability of linear systems.