Some Convergence Properties of Two Iterative Algorithms for Discrete Periodic Lyapunov Equations

• 成果类型: Article
• 署名作者: Chen, Zebin; Chen, Xuesong; Sun, Hui-Jie
• 署名单位: Guangdong University of Technology; Sun Yat Sen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3241189
• 发表日期: 2023
• 页码: 6751-6757
• 关键词: Convergence analysis; iterative algorithm; multiple tuning parameters; periodic Lyapunov matrix equations.

摘要

In this article, 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.