The state-space model of a dynamical system is given as:
x₁˙=x₂
x₂˙=-2x₂+u
y=x₁
The requirement is to design a discrete-time state feedback controller so that the continuous-time system has a closed-loop step response with the damping ratio ς and settling time Ts specification given as:
ς = 0.707 , Ts = 2seconds

a. Determine the controllability of the continuous-time system