The response of a linear system can be decomposed into zero-input response and zero-state response.
Zero-Input Response
The zero-input response is the system output when the input
Understand the zero-input behavior provides interesting insight into a system. For example, if a system is disturbed momentarily from its rest position and the disturbance is then removed, the system will not come back to rest instantaneously. y. In general, it will come back to rest over a period of time and only through a special type of motion that is characteristic of the system. 1
Zero-State Response
The zero-state response refers to the output of a system that results solely from the input signal
It can be modeled as the convolution of the unit impulse response