An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations

In this paper, an implicit iterative algorithm is proposed for solving a class of Lyapunov matrix equations arising in Itô stochastic linear systems. A tuning parameter is introduced in this algorithm, and thus the convergence rate of the algorithm can be changed. Some conditions are presented such...

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Bibliographic Details
Published in:International journal of systems science Vol. 49; no. 2; pp. 425 - 434
Main Authors: Zhang, Ying, Wu, Ai-Guo, Sun, Hui-Jie
Format: Journal Article
Language:English
Published: London Taylor & Francis 25.01.2018
Taylor & Francis Ltd
Subjects:
Algorithms
Convergence
convergence rate
discrete Lyapunov matrix equations
Iterative algorithms
Iterative methods
Linear systems
Matrix methods
Queuing theory
Smith iteration
Tuning
ISSN:0020-7721, 1464-5319
Online Access:Get full text
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Summary:In this paper, an implicit iterative algorithm is proposed for solving a class of Lyapunov matrix equations arising in Itô stochastic linear systems. A tuning parameter is introduced in this algorithm, and thus the convergence rate of the algorithm can be changed. Some conditions are presented such that the developed algorithm is convergent. In addition, an explicit expression is also derived for the optimal tuning parameter, which guarantees that the obtained algorithm achieves its fastest convergence rate. Finally, numerical examples are employed to illustrate the effectiveness of the given algorithm.
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ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2017.1407009