Some comments on steady-state and asymptotic responses

This paper explores the concepts of steady-state, asymptotic and transient response for linear time-invariant systems. While these concepts appear in many texts in circuits and systems, very often precise definitions are not given. In the paper the linear system is assumed to be a continuous-time single-input-single-output (SISO) system, characterized by its transfer function W(s) or impulse response w(t). The forced response of the system is decomposed into three components, the “input” component, the “system” component, and the “interaction” component. For rational transfer functions and transformed inputs, the above concepts are developed in terms of these three components. The concepts are extended to the case where either the system transfer function W(s) or the transformed input U(s) may be nonrational