A necessary condition is a condition that must be present for an event to occur. A sufficient condition is a condition or set of conditions that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event.

Why is a necessary and sufficient condition important?

A sufficient condition guarantees the truth of another condition, but is not necessary for that other condition to happen. A necessary condition is required for something else to happen, but it does not guarantee that the something else happens.

What is the necessary and sufficient condition for stability?

Abstract: The problem of determining the stability of a feedback system in the presence of perturbation is considered. A necessary and sufficient condition under which the perturbed system remains stable is obtained.