Generalization of the Bylov reducibility theorem and some applications (Q944409)

The paper deals with systems of linear differential equations of the form \[ \dot x=A(t)x,\;x\in \mathbb R^n,\;t\geq 0, \] where \(n\in \mathbb N\) and the coefficient matrix \(A(\cdot)\) is piecewise continuous and uniformly bounded on the half-line \(t\geq 0\). The class of all such systems is denoted by \(M_n\) and the author presents a necessary and sufficient condition for the reducibility of a system in \(M_n\) by a generalized transformation to a block triangular system in \(M_n\).