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2005 Multidimensional Schur Coefficients and BIBO Stability
I. Serban, F. Turcu, Y. Stitou, M. Najim
Commun. Inf. Syst. 5(1): 131-142 (2005).


In the framework of BIBO stability tests for one-dimensional (1-D) linear systems, the Schur-Cohn stability test has the appealing property of being a recursive algorithm. This is a consequence of the simultaneously algebric and analytic aspect of the Schur coefficients, which can be also regarded as \textit{reflection coefficients. } In the multidimensional setting, this dual aspect gives rise to two extension of the Schur coefficients that are no longer equivalent. This paper presents the two extensions of the Schur-Cohn stability test that derive from these extended Schur coefficients. The reflection-coefficient approach was recently proposed in the 2-D case as a necessary but non sufficient condition of stability. The Schur-type multidimensional approach provides a stronger condition of stability, which is necessary and sufficient condition of stability for multidimensional linear system. This extension is based on so-called slice function associated to $n$-variable analytic functions. Several examples are given to illustrate this approach.


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I. Serban. F. Turcu. Y. Stitou. M. Najim. "Multidimensional Schur Coefficients and BIBO Stability." Commun. Inf. Syst. 5 (1) 131 - 142, 2005.


Published: 2005
First available in Project Euclid: 7 June 2006

zbMATH: 1134.93407
MathSciNet: MR2199727

Rights: Copyright © 2005 International Press of Boston


Vol.5 • No. 1 • 2005
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