Sensitivity of time response to characteristic ratios

In recent works, it has been shown that the damping of a linear time invariant system relates to the so-called characteristic ratios (/spl alpha//sub k/, k = 1,/spl middot//spl middot//spl middot/,n - 1) which are defined by coefficients of the denominator of the transfer function. However, the exact relations are not yet fully understood. For the purpose of exploring the issue, this paper presents the analysis of time response sensitivity to the characteristic ratio change. We begin with the sensitivity of output to the perturbations of coefficients of the system denominator and then the first order approximation of the /spl alpha//sub k/ perturbation effect is computed by an explicit transfer function. The results are also extended to the two kinds of all-pole systems. Finally, some illustrative examples are given.