The reachable abundance of the linear continuous-time systems

1. Definition of The Unit Reachable Region

     Definition 1. The uint reachable region $R_{r,T}$ is constituted by all the terminal state $x_{T}$ that can be reached from origin of the state space of the linear continuous-time systems with the unit input energy $\left(\left\Vert u_{t}\right\Vert _{\infty}\leq1,t\in[0,T]\right)$ in the finite terminal time $T$ .

2. Definition of The Reachable Abundance

     Definition 2. The reachable abundance is defined as the two-tuples $(r_{T},v_{r,T})$ , where $r_{T}$ and $v_{r,T}$ are the space dimension and the volume of the unit reachable region $R_{r,T}$ , respectively.

     Some results are in my paper arXiv1705.08064(On Controllable Abundance Of Saturated-input Linear Discrete Systems)