Uniform asymptotic integration of a family of linear differential systems

Consider a family of linear differential systems y' = A(x,z)y, depending on a parameter z. Assume, as in Levinson's Theorem, that A = Lambda + R with Lambda diagonal and R integrable. We discuss the problem of asymptotically solving this system with uniform tin z) control on the error terms. Questio ns of this type occur in the spectral theory of differential operators.