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Yesterday, during my exam, I had the following exercise:

Given $$H(s) = \frac{1}{s^2+2s+4}$$ check if it's stable.

which was supposed to be the hardest (since it was the last one). From my knowledge, I quickly found out the poles, checked the real part of the pole (which was $-1$) and said that the system is stable. Is my argument incomplete? Everyone in the classroom seemed to write a lot more at that final exercise.

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Did you mention the region of convergence? The system can be stable, but anti-causal depending on the ROC.

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    $\begingroup$ You could also argue that one can only conclude that this system has a stable observable and controllable part. $\endgroup$
    – fibonatic
    Sep 1, 2017 at 20:34

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