On global Lyapunov reducibility of two-dimensional linear time-invariant control systems

Let the stationary system $\dot x=Ax+Bu, x\in\mathbb{R}^2, u\in\mathbb{R}^m$ is totally controllable. Then it possesses the property of global Lyapunov reducibility in class of stationary controls $u=Ux$, that is for any fixed stationary system $\dot y=Cy$ there exists the time-independent matrix $U$, such that the system $\dot x=(A+BU)x$ with this matrix is asymptotically equivalent (kinematically similar) to the above fixed system.