Given what we now know about state-space and transfer-function representations, we can now relate the characteristic roots (i.e., poles) or system eigenvalues to the features of typical responses such as the natural, impulse, step, and ramp responses. The system parameters affect how quickly a response reaches and settles to steady-state. As one or more parameters of the system are varied, the eigenvalues change and so do the response characteristics. Consider the following:

B How then do the system parameters affect the response?