Simple recursive processes for determining Laplace and Z transforms of the zero-input responses of linear time-invariant systems

Simple recursive methods are derived for quickly and easily writing either the Laplace transform of the zero-input response of a linear time-invariant continuous-time system or the z-transform of the zero-input response of a linear time-invariant discrete-time system. Application of the results to example systems shows that the derived processes make it possible to express the transform of the zero-input response nearly as easily as writing the transform of the zero-state response.