Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-02-10
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
It is well-known that the stability of a first-order autonomous system can be determined by testing the symmetric positive definite solutions of associated Lyapunov matrix equations.
However, the research on the constrained solutions of the Lyapunov matrix equations is quite few.
In this paper, we present three iterative algorithms for symmetric positive semidefinite solutions of the Lyapunov matrix equations.
The first and second iterative algorithms are based on the relaxed proximal point algorithm (RPPA) and the Peaceman–Rachford splitting method (PRSM), respectively, and their global convergence can be ensured by corresponding results in the literature.
The third iterative algorithm is based on the famous alternating direction method of multipliers (ADMM), and its convergence is subsequently discussed in detail.
Finally, numerical simulation results illustrate the effectiveness of the proposed iterative algorithms.
American Psychological Association (APA)
Sun, Min& Liu, Jing. 2020. Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1197494
Modern Language Association (MLA)
Sun, Min& Liu, Jing. Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations. Mathematical Problems in Engineering No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1197494
American Medical Association (AMA)
Sun, Min& Liu, Jing. Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1197494
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197494