Talk:Control Systems/Digital State Space

A question about a formula. Consider such piece of text:

"If we substitute in a new variable β = (k + 1)T + τ, and if we see the following relationship:

e^{akT}*x[0] = x[k]"

And then - final result.

But before there was another formula:

x[k] = e^{akT}*x[0] + {integral from zero to kT of (something...)}

Does it mean, that this "something" is always equal zero? This "something" depends of u(tau), I don't think that it is zero!