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:

$Me^{j\theta }=C(e^{j\omega }I-A)^{-1}B+D$

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 $x(k)=Ge^{j...}$ (you need to figure out this exponent!).

--Elisa