Which name is appropriate for the new measure on the control ability of the dynamical systems

     In control theory field, the rank of the controllable matrix $Q_{c}=[B,AB,\cdots,A^{n-1}B]$ is for investigating the control ability of the dynamic systems $\Sigma(A,B)$ , and that the matrix is full rank means that the systems is the fully state controllable, and then the bigger the rank is, the stronger the control ability of the systems is. Up to now, no precise concept on the control ability is presented.

        In fact, the rank of the controllable matrix and the controllablilty are not good measures on the control ability. For example, for the uncontrollable matrix pair $(A,B)$ , a little perturbation on the matrix $A$ or $B$ may lead to that the matrix pair is controllable. So, there isn't exist a distinct line between the controllability and uncontrollability concepts and the two concepts are fuzzy. Considered that the modeling error for the system models of the practical dynamic systems, the rank of the controllable matrix and the controllability aren't appropriate for investigating precisely the control ability of the practical dynamic systems.

    In the studying on the precise measure on the control ability of the dynamic systems, the volume value of the controllable region under the unit input energy $\left(\left\Vert u_{t}\right\Vert _{\infty}\leq1,\forall t\right)$ is propose as a new precise measure on that in my paper arXiv1705.08064(On Controllable Abundance Of Saturated-input Linear Discrete Systems). A new theorem on the positive relations among the volume value, the diversity of the control laws (i.e., the size of the solution space of the control laws) in the controller designing, and the performances and robustness of the closed-loop control systems is presented and proven in the paper. That is, the bigger the volume value of the controllable region, the richer the control laws, and then t the closed-loop control systems may be with he better performance and robustness. The volume value is a good measure on the control ability.

     How to name the new measure? Which name is appropriate for that, controllable (or controllability) power, controllable (or controllability) abundance, controllable (or controllability) richness, or others? Which colleague gives some helpful suggestions.