Definition of a Stable System
A system is stable if bounded inputs yield bounded outputs. This means if there is an input of x(t) which goes through a system to produce an output y(t), there must be a finite value 'M' such that |x(t)| < M and a finite value 'N' such that |y(t)| < N, for all 't.'
Definition of an Unstable System
A system is considered to be unstable if either the input to the system or the output of the system goes towards infinity. This means that if there is an input x(t) that goes through the system and produces an output y(t) if either the input x(t) goes to infinity or the output y(t) goes to infinity then the system is considered to be unstable.
