Stability
A system is said to be stable if a bounded input yeilds a bounded output. This means that if you can take an input signal whose value does not increase to infinity as x -> infinity, then the output of the system should not go to infinity either.
Unstable
A system is said to be unstable if a bounded input yeilds an unbounded output. This means that if you can take an input signal whose value does not increase to infinity as x -> infinity, then the output of the system will go to infinity if the system is unstable.
