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Can someone explain me what ideal integrator is as simple as possible? Which meaning it has in this diagram?

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$A,B,C$ and $D$ are matrices. $u$ is input and $y$ is output.

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    $\begingroup$ Welcome to SE.DSP! An ideal integrator is just an integrator --- as opposed to a "leaky" one --- it performs integration of the input variable with respect to time. $\endgroup$ – Peter K. May 21 '17 at 0:59
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$x[n] = x[n-1] + x'[n]$ is the discrete time domain difference equation for an ideal integrator. It has a pole on the unit circle at $z=1$, so it is unstable.

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  • $\begingroup$ In my experience (in control) we would typically say that an integrator is marginally stable rather than unstable. $\endgroup$ – Max May 21 '17 at 15:26
  • $\begingroup$ Yes, I was imprecise about the stability. In practice the ideal integrator becomes useless (reaches $\pm \infty$ as far as numerical computation using floating point is concerned) in some amount of time, if the input has a DC offset. $\endgroup$ – Andy Walls May 21 '17 at 16:14

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