1975
DOI: 10.1109/proc.1975.9880
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The theory and applications of the inners

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Cited by 26 publications
(8 citation statements)
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“…In the literature, several tests exist which check various conditions of the coefficients of f(z1; z2) [1], [6]- [8]. From another standpoint, we obtain that most of tests check sufficient conditions for stability [6]- [14], while other tests check necessary stability conditions [15], [17].…”
Section: Introductionmentioning
confidence: 92%
“…In the literature, several tests exist which check various conditions of the coefficients of f(z1; z2) [1], [6]- [8]. From another standpoint, we obtain that most of tests check sufficient conditions for stability [6]- [14], while other tests check necessary stability conditions [15], [17].…”
Section: Introductionmentioning
confidence: 92%
“…These two equations can readily be put in the form of three polynomial equations in the three independent variables x y , ,ω 2 , where x s =Re 1 l q and y s =Im 1 l q. Their common solution(s) can be found, if desired, using the resultant method of these polynomials [16], [39]. In the sequel, one must select as σ 1 the maximum x of all the solutions ( x y , ,ω 2 ).…”
Section: Computation Of the Stability Margins For 2-d Continuous Systemsmentioning
confidence: 99%
“…There exist several algebraic methods for testing the stability of 2-D continuous systems or, equivalently, checking the Hurwitz character of 2-D polynomials [30], [28], [29]. Among them are the table form as advanced by Siljak [13], the determinant method (Anderson-Jury [14]), the inner method [16], [21] as advanced in [24], and the Zeheb-Walach method [12]. Another somewhat tedious approach is the method of the bilinear transformation.…”
mentioning
confidence: 99%
“…One procedure is Sylvester's theory of eliminants [19], but again we quickly encounter polynomials of very high degree [11], and the method is ill-conditioned for even moderate p, rn and n. An alternative is to define P 2 n-1 (R) by P()=-=1 p()2, and to set f= ('zpP)]S"-1. Then f zP(R)IS"-I. Construct an evaluation tree for 504 GEORGE E. BACKUS (Sn-l, , f, qw, a, r) as in Theorem 2.5, with qw as in (5.5) (and p replaced by 2p) and with limi_,oo a (j) limj_,oo r(j) 0.…”
Section: ]Sup F#-mi V ]Inf Fu#-m] =< ]B -M] V Ib -M[ Amentioning
confidence: 99%
“…The generalization of the Sturm algorithm to R" has been discussed extensively in the literature on the stability of electrical and mechanical systems and digital filters, where stability is often decided by whether a certain polynomial is positive everywhere on a certain domain. See, for example, [4], [6], [10], [11], [12]. The last two papers have wide bibliographies.…”
mentioning
confidence: 99%