Conditions for uniform ensemble output controllability, and obstruction to uniform ensemble controllability

Overview & Synopsis

We consider the linear time-invariant system ẋ(t, θ) = A(θ)x(t, θ) + B(θ)u(t) with output y(t, θ) = C(θ)x(t, θ) where A, B and C are continuous matrices with respect to the constant parameter θ, which belongs to some compact set P. Given any continuous initial state datum θ → x₀(θ) and any continuous output function θ → y₁(θ), we investigate the existence of a θ-independent open loop control u such that x₀ is steered, in nite time, arbitrarily closed to y₁ with the uniform norm. When C(θ) is the identity matrix, this notion is usually termed to be uniform ensemble controllability. In this paper, we extend some result on uniform ensemble controllability to the case where C(θ) is not the identity matrix. We will also give some obstructions to ensemble controllability when the parameter set admits an interior point.