What is the controllable abundance of the dynamic systems?

In my paper arXiv1705.08064(On Controllable Abundance Of Saturated-input Linear Discrete Systems)，a new measure on the state control ability of the linear discrete systems is presented as an improving and promoting concept of the state controllability in the control theory field. The new measure is not only used to distinguish the controllability or uncontrollability, but also can be used to meter precisely the state control ability of the systems, and maybe is a fundamental concept and index to the dynamic systems.

Based on the new measure, many works in the control field and other related fields can be developed and new results will be with the significant value. Some works related to the controllable abundance can be listed as follows.

1. By computing and optimizing on the controllable abundance, the dynamics and kinematics of the dynamic systems can be improved and promoted, such as, enhancing the control ability of the input variable, extending the controllable region in the state space, and so on.

2. By computing and comparing on the controllable abundance, the input variables with the better control ability are determined from the candidate variables in the modeling of the controlled plants and the control efficient of the control systems can be promoted.

3. Based on the relation theorem among the control abundance, the control ability, and the size and richness of the solution set of the control laws in the controller designing, when the controlled plants are optimized on the controllable abundance, the closed-loop control systems designing by the conventional control methods can be with the better performance and robustness.

4. The controllable abundance can provide the theoretical basis and method for determine the control horizon, the optimization horizon, the target state, the reference trajectory in the many control methods , such as, optimal control, adaptive control, predictive control , receding horizon optimal control, and so on.

5. The controllable abundance can be used as the objective function (performance index) or the constrained conditions in the optimal control and robust control, and optimizing the control abundance can be promoting the performance and robustness of the closed-loop systems.

6. As the generalization of the controllable abundance concept, the observable abundance can be proposed to meter the observe ability of the dynamic systems and is used to promote the state filtering systems and communication systems.

More meaningful works about the controllable abundance can be proposed and developed, after deeply understanding the new measure and concept.