• / 9
  • 下载费用:10 金币  

Bernstein Bezout矩阵与多项式的惯性.doc

关 键 词:
Bernstein Bezout矩阵与多项式的惯性.doc
资源描述:
Bernstein Bezout Fujiwara-Hermite Routh-Hurwitz Bernstein , Bezout Bernstein Bezout , Bernstein Bezout ; Bernstein . Bernstein ; Bernstein Bezout ; Fujiwara-Hermite ; Routh-Hurwitz ; (1997) , , , . (1966) , , , , , .E-mail:wuhz@ahu.edu.cn. (1208085MA02) Bernstein Bezout Matrix and Polynomial Inertia LI Shan WU Hua-zhang School of Mathematical Sciences, Anhui University; Abstract In order to study the theory of Fujiwara-Hermite and Routh-Hurwitz criteria under the Bernstein polynomials basis, the authors use the algebraic method of the transformation relation between the classical Bezout matrix and Bernstein Bezout matrix to give some investigations on the polynomial inertia and stability theory in terms of the Bernstein Bezout matrix. The results obtained can be viewed as the generalizations of the corresponding classical Fujiwara-Hermite and Routh-Hurwitz criteria to the cases under the Bernstein polynomials basis. Keyword Bernstein polynomials basis; Bernstein Bezout matrix; Fujiwara-Hermite criteria; Routh-Hurwitz criteria; 0 Bezout [1-4], , Bezout [5-8]. Bernstein , Bezier [9-11], . , [12] Bernstein Bezout Bernstein ( ) / . [12] , Bernstein Bezout . , [1] . n-1 . : n . T B (x) , n[x] f (x) g (x) , m=deg Bernstein a (x) b (x) , , a (x) b (x) : B (a, b) = (zij) a (x) b (x) Bezout , B (f, g) . f (x) g (x) Bernstein : B (f, g) = (z ij) f (x) g (x) Bernstein Bezout . (1) , Bezout Bernstein Bezout : S (a) =B (a, 1) , S (f) =B (f, 1) , (2) p (x) ( ) , ( Bernstein ) [12], (4) (5) , Bernstein Bezout B (b) (f, g) Barnett : 1 Bezout , , Lyapunov . Fujiwara-Hermite Routh-Hurwitz [3], Bezout Lyapunov . : p (x) , p (x) , ( ) . , p (x) . , : p (x) , ) p (x) , ( ) . , , . A . A Hermite , A=A, A A . A Hermite ( ) . [3], Lyapunov . In (A) =In (H) . , FujiwaraHermite . 2 Bernstein Bezout 3 : , : , : (6) , : (2) , (7) T . (8) : p (x) , 0, 1, , . Routh-Hurwitz Bernstein . : (9) : F=TDT, 1 , Routh-Hurwitz Bernstein . 4 Bernstein Bernstein Bezout , [1]BARNETT S.Polynomials and Linear Control System[M].New York:Marcel Dekker, 1983 [2]HEINIG G, ROST K.Algebraic Methods for Toeplitz-like Matrices and Operators[M].Basel:Birkhauser, 1984 [3]LANCASTER P, TISMENETSKY M.The Theory of Matrices with Applications[M].2nd New York:Academic Press, 1985 [4]HELMKE U, FUHRMANN P A.Bezoutians[J].Linear Al-gebra and Its Applications, 1989 (122/123/124) :1039-1097 [5]GOVER J, BARNETT S.A Generalized Bezoutian Matrix[J].Linear and Multilinear Algebra, 1990, 27 (11) :33-48 [6]MANI J, HARTWIG R E.Generalized Polynomial Bases and the Bezoutian[J].Linear Algebra and Its Applications, 1997, 251 (12) :293-320 [7]YANG Z H, HU Y J.A Generalized Bezoutian Matrix with Respect to a Polynomial Sequence of Interpolatory Type[J].IEEE Transactions on Automatic Control, 2004, 49 (10) :1783-1789 [8]WU H Z.Generalized Polynomial Bezoutian with Respect to a Jacobson Chain Basis over an Arbitrary Field[J].Linear Algebra and Its Applications, 2010, 432:3351-3360 [9]BINI D A, GEMIGNANI L.Bernstein Bezoutian Matrices[J].Linear Algebra and Its Applications, 2004, 315:319-333 [10]WOLTERS H J, FARIN G E.Geometric Curve Approximation[J].Computer Aided Geometric Design, 1997, 14 (6) :499-513 [11]WINKER J R.The Transformation of the Companion Matrix Resultant Between the Power and Bernstein Polynomial Bases[J].Applied Numerical Mathematics, 2004, 48:113-126 [12] , .Bernstein Bezout / [J]. ( ) , 2017, 34 (2) :12-15ZHENG T T, WU H Z.Connections between Bernstein Bezout Matrix and Generalized Controllability/observability-type Matrices[J].Journal of Chongqing Technology and Business University (Natural Science Edition) , 2017, 34 (2) :12-15
展开阅读全文
  微传网所有资源均是用户自行上传分享,仅供网友学习交流,未经上传用户书面授权,请勿作他用。
0条评论

还可以输入200字符

暂无评论,赶快抢占沙发吧。

关于本文
本文标题:Bernstein Bezout矩阵与多项式的惯性.doc
链接地址:https://www.weizhuannet.com/p-1701.html
微传网是一个办公文档、学习资料下载的在线文档分享平台!

网站资源均来自网络,如有侵权,请联系客服删除!

 网站客服QQ:80879498  会员QQ群:727456886

copyright@ 2018-2028 微传网络工作室版权所有

     经营许可证编号:冀ICP备18006529号-1 ,公安局备案号:13028102000124

收起
展开