On almost reducible systems with almost periodic coefficients

Let $\dot x=A(t)x$ be a system of two linear ordinary differential equations with almost periodic coefficients. Then there exists for any positive $\varepsilon$ an almost reducible system of equations $\dot x=B(t)x$ with almost periodic coefficients and such that
$$ \sup_{-\infty<t<+\infty}\|A(t)-B(t)\|<\varepsilon. $$