Problem 3 (c) -- Errata

From MurrayWiki

In part (c) of this problem you will have to use as input u(k) = sin(ωk), and find the steady state system response. The correct general formula which you should prove is as follows:

Mejθ = C(ejωI − A) − 1B + 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) = ejωk and express the general solution of the difference equation as x(k) = Gej... (you need to figure out this exponent!).

--Elisa

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