Transient & Steady State Response

Systems can be analysed using the system response to an input to the signal. The response of any system is the sum of the transient and the steady state response. Any system can either be in equilibrium or not in equilibrium(rise/decay). The transient response is the response of the system to a change in equilibrium and steady state is the response when the system is in equilibrium.

The term “transient” means “short-lived”. Transient Response is present as soon as we switch on the system but is short lived and approaches 0 as time approaches infinity. This is true as long is the system is asymptotically stable. Then;

So if given a system response, its easy to find which part of the equation is transient or steady state using the above equations. The response curve of a system then consists of both the transient and steady state responses. For instance, in case of the unit-impulse response of a first order system;