Uniform and Lq-ensemble reachability of parameter-dependent linear systems

In this paper, we consider families of linear systems (linear ensembles) defined by matrix pairs (A(θ),B(θ)) depending on a parameter θ∈P that is varying over a compact subset P of the complex plane. In particular, we investigate the existence of open-loop controls which are independent of the parameter θ∈P and steer a given family of initial states x0(θ) arbitrarily close to a desired family of terminal states f(θ) in finite time. Here, the maps θ↦x0(θ) and θ↦f(θ) are assumed to lie in a common appropriately chosen Banach space Xn(P) of Cn-valued functions. If this task is solvable for all initial and terminal states, the pair (A(θ),B(θ)) is called (completely) ensemble controllable with respect to Xn(P).