1. ## final value

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

2. 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

$\displaystyle \chi$ $\displaystyle \sigma$

3. ## more details final value

I need more details