Implicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations

2017 ◽  
Vol 11 (10) ◽  
pp. 1554-1560 ◽  
Author(s):  
Ying Zhang ◽  
Ai-Guo Wu ◽  
Chun-Tao Shao
Keyword(s):  
Iterative Algorithms ◽  
Tuning Parameter ◽  
Matrix Equations ◽  
Lyapunov Matrix ◽  
Lyapunov Matrix Equations

scholarly journals Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Splitting Method ◽  
Iterative Algorithms ◽  
Positive Semidefinite ◽  
Matrix Equations ◽  
Proximal Point ◽  
Alternating Direction ◽  
Lyapunov Matrix ◽  
Lyapunov Matrix Equations ◽  
The Stability ◽  
Constrained Solutions

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.

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