《Modern Control Engineering, Fifth Edition》

Uncontrollable System. An uncontrollable system has a subsystem that is physically disconnected from the input.

Stabilizability. For a partially controllable system, if the uncontrollable modes are stable and the unstable modes are controllable, the system is said to be stabilizable. For example, the system defined by
$$\left[\begin{array}{c}{\dot{x}}_1\\ {\dot{x}}_2\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& ?1\end{array}\right]\left[\begin{array}{l}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{l}1\\ 0\end{array}\right]u$$
is not state controllable. The stable mode that corresponds to the eigenvalue of $?1$ is not controllable. The unstable mode that corresponds to the eigenvalue of 1 is controllable. Such a system can be made stable by the use of a suitable feedback. Thus this system is stabilizable.

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