Pole deviation analysis for digital systems based on second order perturbation theory [digital filter example]

A pole deviation study is presented for digital systems with stability considerations. An analytical expression for computing the second order pole sensitivities is derived, with which the pole modulus deviation is approximated. Based on this approximation, a new measure is defined to evaluate the system stability. A numerical example shows that this measure is a very good approximation of the unsolved classical stability measure and is more accurate than the approach based on the pole sensitivity study.