Lyapunov reducibility for four-dimensional linear stationary control systems in the class of the piecewise-constant control functions

It is proved that if the stationary control system $\dot x=Ax+Bu,$ $x\in\mathbb R^4,$ $u\in\mathbb R^m$ is totally controllable, then for any constant matrix $C$ there exists bounded piecewise-constant matrix $U=U(t)$ such that the matrices $A+BU(t)$ and $C$ are kinematically similar. The constructed control function $U$ is locally bounded with respect to $C$.