Problem $4$:

A second order system is described by a Transfer Function:

$T(s)=\frac{a}{s^2+bs+c}$

and by a system matrix $A$ :

$A=\left[\begin{array}{cc}-k& -4\\ 25& 0\end{array}\right]$

The unit step response of the system exhibits $20\%$ overshoot and steady state error: $e_{ss}=0\mathrm{.}2$

$($a$)$ Determine the constant $k$

$($b$)$ Determine the constants $a,b,c$