UNIT CIRCLE CAUCHY INDEX: DEFINITION, CHARACTERIZATION AND POLYNOMIAL ZERO DISTRIBUTION.

The authors define the unit circle Cauchy index and give some methods for computing it. This provides a systematic view of many problems and results on unit circle positivity, polynomial root distribution, and stability. Results on positivity of polynomials in z and z** minus **1 which are real on vertical z vertical equals 1 are relevant in checking discrete positive realness and the stability of two-dimensional digital filters, while results on the zero distribution of a polynomial relative to the boundary of the unit circle are of relevance in studying the stability of discrete-time systems.