A system is to be stable if the output of the system after fluctions, variation or oscillation, if any, settles at a reasonable value for any change in input or change in disturbance.
A system is said to be 100 percent accurate if the error ( different between input and output ) is zero. An accurate system is costly. There is no point in going for 100 percent accurate system when that much of accuracy is not really required.
Example of accuracy:
When a variation of say 0.2 degree centigrade cannot be sensed by a human being, there is no need to have a home heating system of temperature variation equal to zero.
Speed of Response:
This refers to time taken by the system to respond to the given input and give that as the output. Theoritically the speed of response should be infinity, that is, the system should have an instantaneous response. This requirement is prime concern with follow-up systems.
Any ideal system is perfectly stable, 100 percent accurate and has instantaneous speed of response. Unfortunately, the requirements are incompatiable. Hence there should be a compromise between these requirements.