1.  Root Locus Method

The first and most direct-method is the root locus method . This consists of repeatedly solving the polynomial equation (8.34) for a range of values of in the neighborhood of the origin. Any standard numerical method, such as Newton-Raphson iteration, may be employed for the approximate solution of (8.34). A plot of against then allows us to deduce intervals of stability in the neighborhood of the origin.

2.  Schur Criteria

We shall call the second method we consider the Schur criterion. In fact, several criteria based on theorem of Schur have been proposed unstably the Wilf stability criterion.

We state the criterion for a general degree polynomial, with complex coefficients

where . The polynomial is said to be a Schur polynomial if its root satisfy . Define the polynomials

where is the complex conjugate of and

.