Direct bilinear Routh stability criteria for discrete systems
type: Item
instance of: scholarly article
title: Direct bilinear Routh stability criteria for discrete systems
zbMATH Open document ID: 0546.93060
DOI: 10.1016/S0167-6911(84)80036-5
published in: Systems \& Control Letters
publication date: 1984-01-01T00:00:00Z
review text: From the Routh conditions for Hurwitz polynomials H(s), expressed by the positivity of the coefficients of the continued fraction (CF) expansions of the tangent function of H(s), some equivalent stability conditions for discrete systems are obtained, using the bilinear transformation \(s=(z- 1)/(z+1)\); for example in Theorem 1 it is shown that a real polynomial D(z) is stable (has all its zeros inside the unit circle) iff all the coefficients of the CF in terms of \(s^{-1}=(z+1)/(z-1)\) (or in s) of the discrete tangent function \(\rho_ n(z)=(D(z)-z^ nD(z^{- 1}))/(D(z)+z^ nD(z^{-1}))\) are positive. Some mixed form (in s and \(s^{-1})\) CF expansions are emphasized and three algorithms are derived to obtain the coefficients of the CF (the first has the simplest set up and the third requires the least number of operations). It is also stated that the number of zeros of D(z) inside and outside the unit circle is equal to the number of the positive and negative coefficients of the CF.
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 3871153
zbMATH Keywords: continued fraction expansions
zbMATH Keywords: Routh conditions
zbMATH Keywords: bilinear transformation
zbMATH Keywords: discrete tangent function
author: Yuval Bistritz
MaRDI profile type: Publication
cites work: A direct Routh stability method for discrete system modelling
cites work: A discrete stability equation theorem and method of stable model reduction
cites work: Stable Linear Systems Simplification Via Pade´ Approximations to Hurwitz Polynomials
cites work: Some new results on discrete system stability
cites work: Q5797046
cites work: Q3313735
cites work: Zero location of polynomials with respect to the unit-circle unhampered by nonessential singularities
cites work: Q5657947
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cites work: On the stability of the<tex>A</tex>matrix inside the unit circle
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description: scientific article; zbMATH DE number 3871153