find final value of y(t)
d4/dt4 y(t) + 4 d3/dt3 y(t) + 3 d2/dt2 y(t) + 5 d/dt y(t) + y(t) = r(t)
y(t) output
r(t) input
thanks
The roots of the polynomial $\displaystyle s^{4} + 4\cdot s^{3} + 3\cdot s^{2} + 5\cdot s + 1$ have all negative real part so that we can apply the 'final value theorem' and obtain...
$\displaystyle \lim_{t \rightarrow \infty} y(t) = \lim_{s \rightarrow 0} s\cdot \int_{0}^{\infty} r(t)\cdot e^{-st}\cdot dt$ (1)
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$