FVT (Final Value Theorem):
if all poles are inside the unit circle (unless at 1,0)
$$ \lim_{k \to \infty} x[k] = \lim_{z \to 1} (1 - z^{-1})X(z) $$
$$ x[k]{k=0}= \lim{z \to \infty} X(z) $$
another z-slove : accroding to defination:
PFE method
$$ e_{ss}=\lim_{z->1}(1-z^{-1})\frac{R(z)}{1+GH} \\ e_{ss}=\frac{1}{1+K_p} $$
$$ overshoot = e^{-\frac{\pi \zeta}{\sqrt{1-\zeta^2}}} $$
$$ t_s= \frac{3}{\zeta \omega_n}(5)\\ t_s= \frac{4}{\zeta \omega_n}(2)\\ t_s= \frac{4.6}{\zeta \omega_n}(1) $$