Abstract
The Cauchy index of a rational transfer function evaluated over an interval of the real line has proved a useful tool in various linear systems applications.
In this paper, we define the unit circle Cauchy index and give some computational methods of 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 r and 2-' which are real on lz/ = 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.
In this paper, we define the unit circle Cauchy index and give some computational methods of 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 r and 2-' which are real on lz/ = 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.
| Original language | English |
|---|---|
| Pages (from-to) | 803–818 |
| Journal | SIAM Journal of Applied Math |
| Volume | 44 |
| Issue number | 4 |
| Publication status | Published - Aug 1983 |