Polynomial Stability Test

Block Polynomial Stability Test uses the Shur - Cohn algorithm to determine if all roots of a polynomial are within the unit circle.

Each column of the input matrix u of size M by N contains M coefficients of an individual polynomial:

Arranged in descending order of degree: . The polynomial has order M-1 and positive integer degree exponents.

The block input represents the coefficients of the polynomials as shown in the previous equation. The block always treats the input undirected vector of length M as an M by 1 matrix.

The output is a 1 by N matrix, each column of which contains a value of 1 or 0. A value of 1 means that the polynomial in the corresponding column of the input is stable, that is, the magnitudes of all solutions of are less than 1. The value 0 means that the polynomial in the corresponding column of the input may be unstable, i.e. the value of at least one solution is greater than or equal to 1.

This block is most often used to check the location of the poles of the polynomial polynomial of the denominator of the transfer function .

The poles are the n-1 roots of the denominator polynomial, . If the poles are located outside the unit circle, the transfer function is unstable. As is common in DSP, the above transfer function is given as decreasing values , not .