Stabilizing polynomials by making their higher-order coefficients sufficiently small

Given a polynomial of arbitrary order with positive coefficients, it is shown that the zeros of the polynomial can always be made to lie within the open left half-plane by multiplying each coefficient by an appropriate power of ε>0 and then letting ε become sufficiently small. This result can be applied to dynamic systems whose models may include small parasitic elements, and it can help to determine the effect of these elements on the stability of the system. Moreover, the result illustrates how ignoring small parasitic elements in a circuit can sometimes lead to an erroneous conclusion about its stability. Several circuit examples are given