The response of a linear system can be decomposed into zero-input response and zero-state response.

total response = zero-input response + zero-state response

Zero-Input Response

The zero-input response is the system output when the input , and thus it is the result of internal system conditions (such as energy storage, initial conditions) alone.

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 , under the assumption that all initial conditions of the system are set to zero. 1

It can be modeled as the convolution of the unit impulse response and the input :

See Also

Footnotes

    • Linear Systems and Signals, 3rd Edition, Chapter 2
    2