标题：Closed-form solutions to the nonhomogeneous Yakubovich-transpose matrix equation
作者：Song, Caiqin; Rui, Hongxing; Wang, Xiaodong; Zhao, Jianli
作者机构：[Song, Caiqin; Rui, Hongxing] Shandong Univ, Sch Math, Jinan 250100, Peoples R China.; [Wang, Xiaodong] Harbin Inst Technol, Sch Astronaut, Harbin 1 更多
通讯作者地址：[Rui, HX]Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
来源：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
关键词：Closed-form solution; Transpose matrix equation; Smith normal form;; Parametric solution; Characteristic polynomial
摘要：The nonhomogeneous Yakubovich-transpose matrix equation X - AX(T) B = CY + R, which contains the well-known Kalman-Yakubovich-transpose matrix equation and general discrete Lyapunov-transpose matrix equation as special cases, has many important applications in control system theory. This study presents two methods to obtain the closed-form solutions of the nonhomogeneous Yakubovich-transpose matrix equation. Moreover, the equivalent forms of the solutions are provided and one of the solutions is established with the controllability matrix, the observability matrix and symmetric operator matrix. (C) 2014 Elsevier B.V. All rights reserved.