Editing Exponential stability (section)

==Practical consequences==

An exponentially stable LTI system is one that will not "blow up" (i.e., give an unbounded output) when given a finite input or non-zero initial condition. Moreover, if the system is given a fixed, finite input (i.e., a [[Heaviside step function|step]]), then any resulting oscillations in the output will decay at an [[exponential growth|exponential rate]], and the output will tend [[asymptote|asymptotically]] to a new final, steady-state value. If the system is instead given a [[Dirac delta function|Dirac delta impulse]] as input, then induced oscillations will die away and the system will return to its previous value. If oscillations do not die away, or the system does not return to its original output when an impulse is applied, the system is instead [[marginal stability|marginally stable]].