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  3. consider a linear system i = a.r + bu with output

Consider a linear system i = A.r + Bu with output y = Cx +...

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Accounting

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Consider a linear system i = A.r + Bu with output y = Cx + Du and x(0) = $. Show that for an exponentially weighted sinusoidal complex input u(t) = ucede = ucct[cos(wt) + i sin(wt)] (1 = 0 +iw) such that \I A is invertible, we have y(t) = Ce At [& - (XI A)-'Bue] + [C(AI A)-+B+D](ueet). Consider a linear system i = A.r + Bu with output y = Cx + Du and x(0) = $. Show that for an exponentially weighted sinusoidal complex input u(t) = ucede = ucct[cos(wt) + i sin(wt)] (1 = 0 +iw) such that \I A is invertible, we have y(t) = Ce At [& - (XI A)-'Bue] + [C(AI A)-+B+D](ueet)

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