Why does instability imply poor performance?

In general, instability causes a system to diverge from a desired state. Imagine that the cruise control in a certain car made the cruise control/vehicle system go unstable. In that case, instead of maintaining the set speed, any disturbance (e.g. a hill, wind, a bump in the road) would cause the controlled speed of the car to oscillate and diverge from the desired speed. Since this isn't the performance that is desired, you can consider this to be poor performance. Since all unstable systems have this property, that implies that the performance of unstable systems is poor.

This figure, from Christian Schmid, shows generic behavior of a) a stable system and b) an unstable system.

--Julia Braman 18:57, 1 October 2007 (PDT)