Affiliations: [a] School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China
| [b] Mathematics School, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai, China
| [c] Shanghai University of Finance and Economics Zhejiang College, Zhejiang, China
| [d] School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China
| [e] Supported by the National Natural Science Foundation of China (No. 12071088)
Correspondence:
[*]
Corresponding author. Jieyong Zhou, Mathematics School, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai, 200433, China. E-mail [email protected].
Abstract: Fuzzy singular Lyapunov matrix equations have many applications, but feasible numerical methods to solve them are absent. In this paper, we propose an efficient numerical method for fuzzy singular Lyapunov matrix equations, where A is crisp and semi-stable. In our method, we transform fuzzy singular Lyapunov matrix equation into two crisp Lyapunov matrix equations. Then we solve the least squares solutions of the two crisp Lyapunov matrix equations, respectively. The existence of fuzzy solution is also considered. At last, two small examples are presented to illustrate the validate of the method and two large scale examples that the existing method fails to slove are presented to show the efficiency of the method.
Keywords: Fuzzy, singular Lyapunov matrix equations, semi-stable, Extension method, the least squares solutions
