# What means ideal integrator in this MIMO system state diagram?

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

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

• 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. – Peter K. May 21 '17 at 0:59

$x[n] = x[n-1] + x'[n]$ 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.

• In my experience (in control) we would typically say that an integrator is marginally stable rather than unstable. – Max May 21 '17 at 15:26
• 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. – Andy Walls May 21 '17 at 16:14