On controllability of time-varying linear population systems with parameters in unbounded sets

The ability to finely manipulate a population of structurally identical dynamical systems is important for various emerging applications across a broad spectrum of fields in science and engineering. Robust control of such an ensemble is fundamentally challenging, because individual systems in the ensemble obey the same dynamical law but have different system parameter values, and only a broadcast control can be applied to the entire ensemble. In this paper, we establish controllability conditions for the finite-dimensional time-varying linear ensemble system in a Hilbert space, whose parameters are in an unbounded set. This work extends our previous study in one-parameter families of linear ensemble systems with the parameter lying in a one-dimensional compact set.