Some Convergence Properties of Two Iterative Algorithms for Discrete Periodic Lyapunov Equations
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DOI码：10.1109/TAC.2023.3241189
发表刊物：IEEE Transactions on Automatic Control
关键字：Iterative algorithm, multiple tuning parameters, convergence analysis, periodic Lyapunov matrix equations
摘要：In this paper, some convergence conditions are investigated for the multiple tuning parameters iterative algorithm (MIA) and the single tuning parameter iterative algorithm (SIA), which are proposed to solve the discrete periodic Lyapunov matrix equations related to discrete-time linear periodic systems. First, when all the tuning parameters are selected in the interval (0,1] and the initial conditions are arbitrarily given, it is proven that the MIA is convergent if and only if the discrete-time linear periodic system is asymptotically stable. In particular, when the coefficient matrices of the considered matrix equations are nonnegative, it is shown that the convergence rate of the MIA increases with the tuning parameter increases from 0 to 1. Moreover, the above convergence results derived for the MIA are extended to the SIA. Furthermore, the searching interval of the optimal tuning parameter for the SIA to achieve the fastest convergence rate is narrowed. Finally, two numerical examples are provided to demonstrate the correctiveness of the proposed theoretical results.
第一作者：Zebin Chen
论文类型：期刊论文
通讯作者：Xuesong Chen,Huijie Sun
卷号：68
期号：11
页面范围：6751-6757
是否译文：否
发表时间：2023-10-30
收录刊物：SCI
发布期刊链接：https://ieeexplore.ieee.org/document/10032721
附件：