Stability is the state or quality of being stable, which characterizes bodies or systems in a state of steadiness and equilibrium (Ferguson, 1992, p. 936).
Example:
A simple real-world example of the notion of stability:Consider a cone in different positions on a horizontal surface:
- Case 1: If the cone is disturbed a little, it will fall back to a position on its base. This is an example of negative feedback, or stability.
- Case 2: The cone is stable. However if disturbed, it will roll taking a new stable position. This is an example of marginal or conditional stability.
- Case 3: The slightest disturbance causes the cone to fall and pick up speed, until flat on its side. This is an example of positive feedback or instability.
A simple real-world example of an unstable system:Consider an amplification system, such as a microphone and loudspeakers. The microphone picks up sound (voice) signals, which are converted to digital signals, amplified by electronic machinery, and then converted back to sound (mechanical) signals to be broadcasted by the loudspeakers.
In any room, small sounds exist forming “noise” in the background. This noise is picked up by the microphone, amplified, and pumped out through the speakers. The once amplified noise coming from the speakers is picked up by the microphone, amplified, and pumped out of the speakers again. That greater amplified noise is once more picked up by the microphone, and goes through the same process over and over. The high speed of the process produces a shriek. The system eventually breaks down due to the increasing pressure and strain the process puts on it (Feedback and Crowding, 2000).
Implications of Stability:
Lathi explains that all practical signal processing signals have to be 
asymptotically stable. Unstable signal processing systems are useless, because any sort of intended or unintended initial input results in an unbounded output that destroys the system. Even though the intended initial input in zero, small noise signals generated within the system will act as (unintended) initial input. Exponential growth in unstable systems cause the initial signal, no matter how small, to eventually result in an unbound output (2005, p. 214).
The result of an unstable system in theory is an output response that tends to infinity. However, in the real world, the result of an unstable system and its output response can be catastrophic.
References
Ferguson, J.G. (1992). Webster's Dictionary. New York: Pamco Publishing Company, Inc.
Feedback and Crowding (2000). Stability and Instability.
Retrieved October 12, 2006, from http://www.abelard.org/feedback.htm
Lathi, B.P. (2005). Linear Systems and Signals(2nd ed.). New York: Oxford University Press
