# STABILITY

Stability is a very important scientific concept  that anyone can and should understand.

Put very simply, a system is stable if it tends towards a point of equilibrium on its own accord i.e. by its design. That is equilibrium is reached without having to add energy or effort to the system.

1. A stable system:  A ball in a bowl will rest at the bottom, if you push the ball it will always return to its original position of rest at the bottom of the bowl.

2. An unstable system:A ball sitting on top of a bowl that is overturned, if you push the ball it will roll down the side of the bowl and to anywhere but its original position of rest. Such a system will always require external effort to return the ball to its original position.

The above examples express stability in terms of a system receiving inputs (pushing of the ball) that produce outputs (a movement of the ball) and that tend to revert back to a point of equilibrium due to the design of the system itself. If the values of the inputs and outputs are "limited" by the design of the system itself, then it is said that they are "bounded" values.

In Control Systems Engineering, a system is considered "stable" when both its inputs and outputs are bounded values, hence the term "Bounded Input Bounded Output" or simply BIBO for short.

# PASSIVITY

A special case of a BIBO system, is where not only are inputs and outputs bounded, but also where outputs never exceed inputs. Such a system is said to be a "Passive" system because the system does not "produce" anything to increase the output beyond the input. All Passive systems are by definition BIBO systems but not all BIBO systems are Passive.

BIBO stability applies to all physical or logical systems of any scope or complexity. As you will find in this document, currency systems can be designed to be Passive BIBO compliant without loss of functionality whatsoever.  Please see the Passive BIBO Currency Standard.