In the theory of system, we know that a system can be BIBO stable but not internally stable (if there is a pole-zero cancellation in the transfer function for example). I find this concept quite difficult to understand. So I'm looking for a concrete example of such a system in the real world.

  • $\begingroup$ Real life devices cannot contain infinity within themselves. So nothing must be unstable. $\endgroup$ May 24, 2015 at 19:11
  • $\begingroup$ Well take any unstable "real world" system. Add some sensors (outputs) to it that don't measure any of the states which blow up. I must admit though that this is a rather artificial way of generating examples for the kind of system you are interested in. $\endgroup$
    – Calculon
    May 24, 2015 at 19:15
  • $\begingroup$ @grdgfgr how about an inverted pendulum? $\endgroup$
    – Calculon
    May 24, 2015 at 19:16
  • $\begingroup$ @Calculon It is clearly unstable. I was saying that you couldn't have intermediate instability and have your system be stable. $\endgroup$ May 24, 2015 at 19:21


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