Polynomial Stability Test

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

Each column of the input matrix size on contains coefficients of an individual polynomial:

Arranged in descending order of degree: . The polynomial has the order and whole positive degree indicators.

The Input of the block represents the coefficients of the polynomials, as shown in the previous equation. The block always considers the input undirected vector of length as a matrix to `1'.

The output is a matrix 1 on , each column of which contains the value 1 or 0'. The value `1 means that the polynomial in the corresponding Input column is stable, that is, the values of all solutions less than 1'. The value `0 means that the polynomial in the corresponding Input column may be unstable, that is, the magnitude of at least one solution greater than or equal to `1'.

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

The poles are roots of the denominator polynomial, . If the poles are located outside the unit circle, the transfer function unstable. As is customary in DSP, the above transfer function is given in the form of decreasing values , and not .