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In this paper, we study the control of a class of time-invariant linearensemble systems whose natural dynamics are linear in the system parameter.This class of ensemble control systems arises from practical engineering andphysical applications, such as transport of quantum particles and control ofuncertain harmonic systems. We establish explicit algebraic criterions toexamine controllability of such ensemble systems. Our derivation is based onthe notion of polynomial approximation, where the elements of the reachable setof the ensemble system are represented in polynomials of the system parameterand used to approximate the desired state of interest. In addition, wehighlight the role of the spectra of the system matrices play in thedetermination of ensemble controllability. Finally, illustrative examples andnumerical simulations for optimal control of this class of linear ensemblesystems are presented to demonstrate the theoretical results.

Ensemble Control of Time-Invariant Linear Systems with Linear Parameter Variation