ON THE ROOTS OF A REAL POLYNOMIAL INSIDE THE UNIT CIRCLE AND A STABILITY FOR LINEAR DISCRETE SYSTEMS
Abstract
Necessary and sufficient algebraic conditions for the roots of a real polynomial to lie inside the unit circle, in a table form, are given. In this form, the constraints are obtained only by evaluation of second order determinants. The connection and identity between the stability criterion established and of a previously obtained criterion are compared. The table is valuable if the coefficients of the real polynomial are given in numbers. Conditions on the numbers of the roots inside, outside, or on the unit circle are also discussed under the cases when the determinants are zero or non-zero. Necessary and sufficient conditions are formulated for all the roots to be inside a circle of radius sigma or less than unity, and also the conditions when the roots are to lie between plus and minus unity in the z-plane. Various examples from discrete systems are presented which illustrate the applications of the new stability criterion and the other conditions formulated in this report. In the conclusion, the various analytical stability criteria applied to linear discrete systems are compared, with emphasis on the advantageous applications of each of the criteria.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 26, 1961
- Accession Number
- AD0277000
Entities
People
- E.i. Jury
- J. Blanchard
Organizations
- University of California, Berkeley