In signal processing and control theory, the Jury stability criterion is a method of determining the stability of a linear discrete time system by analysis of the coefficients of its characteristic polynomial. It is the discrete time analogue of the Routh–Hurwitz stability criterion. The Jury stability criterion requires that the system poles are located inside the unit circle centered at the origin, while the Routh-Hurwitz stability criterion requires that the poles are in the left half of the complex plane. The Jury criterion is named after Eliahu Ibraham Jury.
Contents
Method
If the characteristic polynomial of the system is given by
then the table is constructed as follows:
That is, the first row is constructed of the polynomial coefficients in order, and the second row is the first row in reverse order and conjugated.
The third row of the table is calculated by subtracting
The expansion of the table is continued in this manner until a row containing only one non zero element is reached.
Note the
Stability test
If
Sample implementation
This method is very easy to implement using dynamic arrays on a computer. It also tells whether all the modulus of the roots (complex and real) lie inside the unit disc. Vector v contains the real coefficients of the original polynomial in the order from highest degree to lowest degree.