An approach to determine the stability interval of the constant term of a characteristic equation (Q1085569)

An approach is introduced to determine the stability interval of the constant term of a characteristic equation by using the theory of extended graphical representation of polynomials. Because the constant \(a_ n\) itself is not taken into account and because this method is to get a stability interval of \(a_ n\), not merely to make a stability test for a set of known coefficients, this method of stability criteria has some advantages over the others. The interval of \(a_ n\) can be obtained from the calculation of some algebraical expressions when \(n\leq 10\), where n is the degree of the characteristic equation. It is very convenient to calculate for the cases \(n=5\) and \(n=6\). When \(n\geq 11\), this interval can be found only by the method of numerical solutions.