A moment-based approach to ensemble controllability of linear systems

In this paper we introduce a new perspective on the L²-ensemble controllability problem of linear time-invariant systems using an ℓ²-framework. The reformulation results from focussing on the controllability of the ensemble's moments, which evolve under a linear system defined on the space of square-summable sequences. For a specific class of ensembles, a necessary and sufficient condition can be stated in terms of truncations of infinite Kalman matrices. We illustrate the analysis in this framework on several examples which highlight the possibility of using elementary structural arguments in proving or disproving the controllability of an ensemble's moments, as well as essential differences to the uniform ensemble controllability property which is mostly considered in the literature.