A quadratic bilinear equation arising from the quadratic dynamical system

被引：0

作者：

Yu, Bo ^{[1
]}

Dong, Ning ^{[1
]}

Tang, Qiong ^{[1
]}

机构：

[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412008, Peoples R China

来源：

PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES | 2021年 / 70卷 / 03期

关键词：

quadratic bilinear system; Kronecker product; Hadamard product; existence of the solution; fixed-point iteration; MODEL ORDER REDUCTION;

D O I：

10.3176/proc.2021.3.04

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A quadratic dynamical system with practical applications is taken into consideration. This system is transformed into a new bilinear system with Hadamard products by means of the implicit matrix structure. The corresponding quadratic bilinear equation is subsequently established via the Volterra series. Under proper conditions, the existence of the solution to the equation is proved by using a fixed-point iteration. Numerical experiments verify the proposed theory of the solution.

引用

页码：248 / 259

页数：12

共 24 条

[1] [Anonymous], 1991, Topics in Matrix Analysis
[2] Antoulas. A. C., 2005, Adv. Des. Control
[3] Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
Astrid, Patricia
Weiland, Siep
Willcox, Karen
Backx, Ton
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (10) : 2237 - 2251
[4] An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations
Barrault, M
Maday, Y
Nguyen, NC
Patera, AT
[J]. COMPTES RENDUS MATHEMATIQUE, 2004, 339 (09) : 667 - 672
[5] Benner P., 2017, ARXIV170500160V1MATH
[6] Bhatia R., 1997, MATRIX ANAL
[7] Brennan C, 2006, MATH INDUST, V8, P114
[8] Bubnicki Z., 2005, Modern control theory
[9] Newton's method for a rational matrix equation occurring in stochastic control
Damm, T
Hinrichsen, D
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 332 : 81 - 109
[10] Damm T., 2004, RATIONAL MATRIX EQUA

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