Stability testing of 2-d discrete linear systems by telepolation of an immittance-type tabular test

Research output: Contribution to journalArticlepeer-review

Abstract

A new procedure for deciding whether a bivariate (two-dimensional, 2-D) polynomial with real or complex coefficients does not vanish in the closed exterior of the unit bi-circle (is "2-D stable") is presented. It simplifies a recent immittance-type tabular stability test for 2-D discrete-time systems that creates for a polynomial of degree (n 1, n 2) a sequence of n 2 (or n 1) centro-symmetric 2-D polynomials (the "2-D table") and requires the testing of only one last one dimensional (1-D) symmetric polynomial of degree 2n 1n 2 for no zeros on the unit circle. It is shown that it is possible to bring forth (to "telescope") the last polynomials by interpolation without the construction of the 2-D table. The new 2-D stability test requires an apparently unprecedentedly low count of arithmetic operations. It also shows that stability of a 2-D polynomial of degree (n 1, n 2) is completely determined by n 1n 2 + 1 stability tests (of specific form) of 1-D polynomials of degrees n 1 or n 2 for the real case (or 2n 1 n 2 + 1 polynomials in the complex cases).

Original languageEnglish
Pages (from-to)840-846
Number of pages7
JournalIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume48
Issue number7
DOIs
StatePublished - Jul 2001

Keywords

  • Discrete-time systems
  • Immittance algorithms
  • Multidimensional digital filters
  • Multidimensional systems
  • Stability
  • Stability criteria

Fingerprint

Dive into the research topics of 'Stability testing of 2-d discrete linear systems by telepolation of an immittance-type tabular test'. Together they form a unique fingerprint.

Cite this