$u[k]=-K^{k**}x[k]$ such that the closed $-$ loop behavior shows a dead $-$ beat response. $($b$)$ Now suppose that there is an inevitable delay such that the control action effects the system after one sample delay $u[k]=-K^{*****}x[k-1]i.$ Find a state $-$ space model for the closed $-$ loop system in this case $($Hint: controller now has a memory$).$ Use the same gain you computed in previous part. ii$.$ Compute the eigenvalues of this new closed $-$loop system. iii. Determine if this new system is Reachable or not.