Reducibility and generalized reducibility of linear differential systems with a real multiplier parameter (Q2188046)

Two linear piecewise continuous linear non-autonomous differential systems with bounded coefficients are called reducible or mutually reducible in the general sense, provided that the conjugated coordinates substitution is of Lyapnov-Perron type. Previously, Barabanov had constructed two systems \[ \dfrac{dx}{dt}= A(t)x,\quad \dfrac{dx}{dt}= B(t)x, \] which are reducible, but \[ \dfrac{dx}{dt}= \mu A(t)x,\quad \dfrac{dx}{dt}=\mu B(t)x, \] are not reducible in the both classical and general sense for \(\mu=1/2\). Furthermore, the author presents two reducible systems, which are not reducible in the general sense for \(\mu =(2l+1)/2\) and \(l\in \mathbb{Z}\).