TY - JOUR

T1 - Bounded-Input bounded-output stability tests for two-dimensional continuous-time systems

AU - Bistritz, Yuval

N1 - Publisher Copyright:
© 2004-2012 IEEE.

PY - 2021/5

Y1 - 2021/5

N2 - This paper presents two efficient algorithms to determine whether a bivariate polynomial, possibly with complex coefficients, does not vanish in the cross product of two closed right-half planes (is "2-C stable"). A 2-C stable polynomial in the denominator of a two-dimensional analog filter has been proved (not long ago) to imply bounded-input bounded-output (BIBO) stability. The two algorithms are entirely different but both rely on a recently proposed fraction-free (FF) Routh test for complex polynomials in this transaction. The first algorithm tests the 2-C stability of a bivariate polynomial of degree (n1, n2) in order n6 of elementary operations (when n1 = n2 = n). It is a "tabular type"two-dimensional stability test that can be regarded as a "Routh table"whose scalar entries were replaced by univariate polynomials. The second 2-C stability test is obtained from the first by its telepolation. It carries out the 2-C stability test by a finite collection of FF Routh tests and requires only order n4 elementary operations. Both algorithms possess an integerpreserving property that enhances them with additional merits including numerical error-free decision on 2-C stability.

AB - This paper presents two efficient algorithms to determine whether a bivariate polynomial, possibly with complex coefficients, does not vanish in the cross product of two closed right-half planes (is "2-C stable"). A 2-C stable polynomial in the denominator of a two-dimensional analog filter has been proved (not long ago) to imply bounded-input bounded-output (BIBO) stability. The two algorithms are entirely different but both rely on a recently proposed fraction-free (FF) Routh test for complex polynomials in this transaction. The first algorithm tests the 2-C stability of a bivariate polynomial of degree (n1, n2) in order n6 of elementary operations (when n1 = n2 = n). It is a "tabular type"two-dimensional stability test that can be regarded as a "Routh table"whose scalar entries were replaced by univariate polynomials. The second 2-C stability test is obtained from the first by its telepolation. It carries out the 2-C stability test by a finite collection of FF Routh tests and requires only order n4 elementary operations. Both algorithms possess an integerpreserving property that enhances them with additional merits including numerical error-free decision on 2-C stability.

KW - Bivariate polynomials

KW - Integer algorithms

KW - Routh test

KW - Two-dimensions stability

KW - Very strict Hurwitz polynomials

UR - http://www.scopus.com/inward/record.url?scp=85102263282&partnerID=8YFLogxK

U2 - 10.1109/TCSI.2021.3059839

DO - 10.1109/TCSI.2021.3059839

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AN - SCOPUS:85102263282

SN - 1549-8328

VL - 68

SP - 2134

EP - 2147

JO - IEEE Transactions on Circuits and Systems I: Regular Papers

JF - IEEE Transactions on Circuits and Systems I: Regular Papers

IS - 5

M1 - 9369853

ER -