Parametric solutions to Sylvester-conjugate matrix equations

Authors:
Ai-Guo Wu;Lingling Lv;Guang-Ren Duan;Wanquan Liu
Affiliations:
Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China;Institute of Electric Power, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, PR China;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China;Department of Computing, Curtin University, Purth, Australia
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 4
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Abstract

By two recently proposed operations with respect to complex matrices, a simple explicit solution to the Sylvester-conjugate matrix equation is given in a finite series form. The obtained solution can also be equivalently expressed in terms of the so-called controllability-like matrix and observability-like matrix. The proposed solution can provide all the degrees of freedom which is represented by a free parameter matrix. An illustrative example is employed to show the effectiveness of the proposed method.