Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations
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 p...
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| Veröffentlicht in: | Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-10 |
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| creator | Sun, Min Liu, Jing |
| description | 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. |
| doi_str_mv | 10.1155/2020/6968402 |
| format | Article |
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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.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2020/6968402</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Algorithms ; Computer simulation ; Control theory ; Convergence ; Convex analysis ; Engineering ; Iterative algorithms ; Iterative methods ; Matrix methods ; Methods ; Numerical analysis ; Optimization ; Parameter estimation ; System theory</subject><ispartof>Mathematical problems in engineering, 2020, Vol.2020 (2020), p.1-10</ispartof><rights>Copyright © 2020 Min Sun and Jing Liu.</rights><rights>Copyright © 2020 Min Sun and Jing Liu. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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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. 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| subjects | Algorithms Computer simulation Control theory Convergence Convex analysis Engineering Iterative algorithms Iterative methods Matrix methods Methods Numerical analysis Optimization Parameter estimation System theory |
| title | Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations |
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