翻訳と辞書 Words near each other ・ Bistricioara River (Siret) ・ Bistricë (river) ・ Bistriflimide ・ Bistriji ili tuplji čovek biva kad... ・ Bistrik – Crkvenjak ・ Bistrilitsa ・ Bistrinci ・ Bistrishko Branishte ・ Bistrispinaria ・ Bistritsa ・ Bistritsa Babi ・ Bistritsa, Blagoevgrad Province ・ Bistritsa, Kyustendil Province ・ Bistritsa, Sofia ・ Bistritz ・ Bistritz stability criterion ・ Bistrivode ・ Bistričica ・ Bistrișoara River ・ Bistrița ・ Bistrița (disambiguation) ・ Bistrița Bârgăului ・ Bistrița ghetto ・ Bistrița Monastery ・ Bistrița Monastery (disambiguation) ・ Bistrița Monastery (Vâlcea) ・ Bistrița Mountains ・ Bistrița River ・ Bistrița River (Danube) ・ Bistrița River (Iza) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bistritz stability criterion ： ウィキペディア英語版 Bistritz stability criterion In signal processing and control theory, the Bistritz criterion is a simple method to determine whether a discrete linear time invariant (LTI) system is stable proposed by Yuval Bistritz.〔Y. Bistritz (1984) ( Zero location with respect to the unit circle of discrete-time linear system polynomials ), Proc. of the IEEE, 72 (9): 1131–1142.〕〔Y. Bistritz (2002) ( Zero location of polynomials with respect to the unit circle unhampered by nonessential singularities ), IEEE Trans. CAS I, 49(3): 305–314.〕 Stability of a discrete LTI system requires that its characteristic polynomials :$D\_n(z)=d\_0+d\_1\; z+d\_2\; z^2+\; \backslash cdots\; +\; d\_z^\; +\; d\_n\; z^n$ (obtained from its difference equation, its dynamic matrix, or appearing as the denominator of its transfer function) is a stable polynomial, where $D\_n(z)$ is said to be stable if all its zeros are inside the unit circle, viz. :, where $D\_n(z)=d\_n\; \backslash prod\_^n\; (z-z\_k)$. The test determines whether $D\_n(z)$ is stable algebraically (i.e. without numerical determination of the zeros) . The method also solves the full zero location (ZL) problem. Namely, it can count the number of inside the unit-circle (IUC) zeros , on the unit-circle zeros (UC) zeros $(~\; |\; z\_k|\; =\; 1\; ~)$ and outside the unit-circle (OUC) zeros $(~\; |\; z\_k|\; >\; 1\; ~)$ for any real or complex polynomial.〔〔 The Bistritz test is the discrete equivalent of Routh criterion used to test stability of continuous LTI systems. This title was introduced soon after its presentation.〔E. I. Jury and M. Mansour (1985), ( On the terminology relationship between continuous and discrete systems criteria ), Proc. of the IEEE, 73(4):884.〕 It has been also recognized to be more efficient than previously available stability tests for discrete systems like the Schur–Cohn and the Jury test.〔K. Premaratne, and E. I. Jury (1993) (On the Bistritz tabular form and its relationship with the Schur–Cohn minors and inner determinants ), J. of the Franklin Institute, 30(1):165-182.〕 In the following, the focus is only on how to test stability of a real polynomial. However, as long as the basic recursion needed to test stability remains valid, ZL rules are also brought. ==Algorithm== Consider $D\_n(z)$ as above and assume $D\_n(1)\; \backslash neq\; 0$. (If $D\_n(1)=0$ the polynomial is not stable.) Define its reciprocal polynomial :$D^\backslash sharp\_n(z)=z^n\; D\_n(1/z)=d\_n+d\_z+d\_\; z^2+\backslash cdots+d\_z^\; +\; d\_0\; z^n$. The algorithm assigns to $D\_n(z)$ a sequence of symmetric polynomials :$T\_m(z)=T^\backslash sharp\_m(z),\; m=n,n-1,\; \backslash ldots\; ,\; 0$ created by a three-term polynomial recursion. Write out the polynomials by their coefficients, :$T\_m(z)=\backslash sum\_^m\; t\_\; z^k$, symmetry means that :$T\_m(z)=t\_+t\_\; z\; +\; \backslash cdots\; +\; t\_\; z^+t\_\; z^m$, so that it is enough to calculate for each polynomial only about half of the coefficients. The recursion begins with two initial polynomials driven from the sum and difference of the tested polynomial and its reciprocal, then each subsequent polynomial of reduced degree is produced from the last two known polynomials. Initiation: : $T\_n(z)=D\_n(z)+D^\backslash sharp\_(z)\; \backslash quad,\; \backslash quad\; T\_(z)=\backslash frac$ Recursion: For $m=n-1,\backslash ldots,1$ do: : $\backslash delta\_=\backslash frac$ : $T\_(z)=\backslash frac(z)\; \}$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bistritz stability criterion」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.