Stability testing of two-dimensional discrete linear system polynomials by a two-dimensional tabular form

Research output: Contribution to journalArticlepeer-review

Abstract

A new test for determining whether a bivariate polynomial does not vanish in the closed exterior of the unit bicircle (is stable) is developed. A stable bivariate polynomial is the key for stability of two-dimensional (2-D) recursive linear discrete systems. The 2-D stability test stems from a modified stability test for one-dimensional (1-D) systems that has been developed by the author. It consists of a 2-D table, a sequence of centro-symmetric matrices, and a set of accompanying necessary and sufficient conditions for 2-D stability imposed on it. The 2-D table is constructed by a three-term recursion of these matrices or corresponding bivariate polynomials. The minimal set of necessary and sufficient conditions for stability consists of testing two univariate polynomial, one before and one after completing the table, for no zeros outside and no zeros on the unit circle, respectively. A larger set of useful conditions that are necessary for 2-D stability, and may indicate earlier instability, is also shown.

Original languageEnglish
Pages (from-to)666-676
Number of pages11
JournalIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume46
Issue number6
DOIs
StatePublished - 1999

Fingerprint

Dive into the research topics of 'Stability testing of two-dimensional discrete linear system polynomials by a two-dimensional tabular form'. Together they form a unique fingerprint.

Cite this