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Homework Statement
Where $$v = y - bu$$
It's given that the transfer function is
$$h(t) = b u(t) + v(t) = b \delta(t) + e^{at}b \mu(t)$$
Homework Equations
The Attempt at a Solution
I can't seem to figure out how the impulse response above was found. I understand that the impulse response is y when ##u = \delta(t)##, but I'm not sure where the exponential comes from. One of the steps in the problem is
$$
y(t) = bu(t) + \int_{t_{0}}^{t} e^{a(t-\tau)} abu (\tau) d \tau
$$
where the second term on the right is v. Going by the diagram, shouldn't v be equal to the following?
$$
v = \int_{t_{0}}^{t} u(\tau) ab + v(\tau)a \; d\tau
$$
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