We establish that the reducibility exponent (
Differentsial’nye Uravneniya, 2007, vol. 43, no. 2, pp. 191–202) of each linear system
$$\dot x = A(t)x, x \in \mathbb{R}^n , t \geqslant 0$$
, with piecewise continuous bounded coefficient matrix
A does not belong to the set of values of
σ for which the perturbed system (1
A+Q) with an arbitrary piecewise continuous perturbation
Q satisfying the condition
\(\overline {\lim } _{t \to + \infty } t^{ - 1} \ln \left\| {Q(t)} \right\| \leqslant - \sigma \) is reducible to the original system (1
A ) by some Lyapunov transformation.