The map R^{2T} to W^T via C^T factorization is continuous in operator topologies, so R_j^{2T} converging implies the potential q_j converging to q in H^{-2}(Ω^T).
Local controllability in classes of differentiable functions for the wave equation.Journal of Mathematical Sciences, Vol
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On a stability of time-optimal version of the Boundary Control method
The map R^{2T} to W^T via C^T factorization is continuous in operator topologies, so R_j^{2T} converging implies the potential q_j converging to q in H^{-2}(Ω^T).