System of differential equations - stationary solution given u(t) = sin(t) I have a system of differential equations given by: 
$$x'= Ax+bu$$
$$y = d^Tx$$
I have then been told that if I have an external force $u(t) = e^{st}$,  then the stationary solution is given by: $y(t) = H(s) e^{st} $. My question then is what the stationary solution will be if i have an external force given by $ u(t) = \sin(kt) $ or $ \cos(kt) $ for that sake? 

As long as $\pm ik$ are not eigenvalues of $A$, the "stationary solution" will be of the form $a(k) \cos(kt) + b(k) \sin(kt)$.
