Controllability of linear ensemble systems with constant drift and linear parameter variation

Control of population systems is an indispensable task in many cutting-edge applications from nuclear magnetic resonance spectroscopy and imaging to deep brain stimulation for treatment of neurological disorders. Characterizing the fundamental limit of the ability to control such large-scale systems is critical towards the understanding of their functionality and dynamical structures. In this paper, we study controllability of time-invariant linear ensemble systems whose natural and control dynamics form a linear variety of the system parameter. We derive explicit controllability conditions in terms of the rank of the system and control matrices, and show that ensemble controllability is highly dependent on the spectrum structure of the parameter-dependent system matrix.