On Uniform Ensemble Controllability of Diagonalizable Linear Ensemble Systems

Abstract: In this paper, we study uniform ensemble controllability (UEC) of linear ensemble systems defined in an infinite-dimensional space through finite-dimensional settings. Specifically, with the help of the Stone-Weierstrass theorem for modules, we provide an algebraic framework for examining UEC of linear ensemble systems with diagonalizable drift vector fields through checking the controllability of finite-dimensional subsystems in the ensemble. The new framework renders a novel concept of ensemble controllability matrix, which rank-condition serves as a sufficient and necessary condition for UEC of linear ensembles. We provide several examples demonstrating that the proposed approach well-encompasses existing results and analyzes UEC of linear ensembles not addressed by literature.