Problem 3 (c) -- Errata

In part (c) of this problem you will have to use as input \(u(k)=sin(\omega k)\), and find the steady state system response. The correct general formula which you should prove is as follows\[M e^{j\theta}=C(e^{j\omega}I-A)^{-1}B + D\]

Hint: assume that \(u(k)=sin(\omega k)=\mathcal{I}m(e^{j\omega k})\).

You can therefore find the solution in the required form by using the Euler formulas: use \(u(k)=e^{j\omega k}\) and express the general solution of the difference equation as \(x(k)= G e^{j ...}\) (you need to figure out this exponent!).

--Elisa