Problem 3 (c) -- Errata

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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