Some new results on the controllable abundance of linear discrete systems

1. Computing method of the finite-time controllable abundance $$ $(r_{T},v_{c,T})$ for the linear discrete systems with any dimensions

2. Recursive computing method of the finite-time controllable abundance $$ $(r_{T},v_{c,T})$ for the linear discrete systems with any dimensions；

3. Computing method of the infinite-time controllable abundance $(r_{\infty},v_{c,\infty})$ for the linear discrete systems with $n$ distict and real eigenvalues

4. Computing method of the controllable abundance $$ $(r_{T},v_{c,T})$ for the 2- or 3-dimensions linear discrete systems with a pair of complex eigenvalues, include the finite-time and the infinite-time cases.