On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW

On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW

This paper considers the solution to a class of the second-order Sylvester matrix equation EVF2−AVF−CV=BW. Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal fo...

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Main Authors: Wang Guo-Sheng, Lv Qiang, Duan Guang-Ren
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2007/21078
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spelling doaj-15b2db4a595b410096669a99901f87f02020-11-24T23:17:07ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472007-01-01200710.1155/2007/2107821078On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BWWang Guo-Sheng0Lv Qiang1Duan Guang-Ren2Department of Control Engineering, Academy of Armored Force Engineering, Beijing 100072, ChinaDepartment of Control Engineering, Academy of Armored Force Engineering, Beijing 100072, ChinaCenter for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, ChinaThis paper considers the solution to a class of the second-order Sylvester matrix equation EVF2−AVF−CV=BW. Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.http://dx.doi.org/10.1155/2007/21078
collection DOAJ
language English
format Article
sources DOAJ
author Wang Guo-Sheng
Lv Qiang
Duan Guang-Ren
spellingShingle Wang Guo-Sheng
Lv Qiang
Duan Guang-Ren
On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW
Mathematical Problems in Engineering
author_facet Wang Guo-Sheng
Lv Qiang
Duan Guang-Ren
author_sort Wang Guo-Sheng
title On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW
title_short On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW
title_full On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW
title_fullStr On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW
title_full_unstemmed On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW
title_sort on the parametric solution to the second-order sylvester matrix equation evf2−avf−cv=bw
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2007-01-01
description This paper considers the solution to a class of the second-order Sylvester matrix equation EVF2−AVF−CV=BW. Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.
url http://dx.doi.org/10.1155/2007/21078
work_keys_str_mv AT wangguosheng ontheparametricsolutiontothesecondordersylvestermatrixequationevf2avfcvbw
AT lvqiang ontheparametricsolutiontothesecondordersylvestermatrixequationevf2avfcvbw
AT duanguangren ontheparametricsolutiontothesecondordersylvestermatrixequationevf2avfcvbw
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