Iterative solvers for periodic matrix equations and model reduction for periodic control systems
Iterative solvers for periodic matrix equations and model reduction for periodic control systems
复制标题
周期矩阵方程的迭代求解器和周期控制系统的模型简化
DOI：
10.1109/icece.2012.6471669
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
P. Benner
中科院分区：
文献类型：
--
作者：
M. Hossain;P. Benner
各种工程和机械问题的周期控制系统的分析和综合与众所周知的矩阵方程密切相关，即，李雅普诺夫或黎卡提方程。本文提出了求解周期广义系统的周期状态反馈控制问题和模型降阶问题中的大规模稀疏投影离散时间周期Lyapunov方程的迭代方法。我们将交替方向隐式方法和Smith方法推广到这类方程，并讨论了它们在周期广义系统模型降阶过程中的应用。数值结果表明了该方法的有效性和准确性。
Analysis and synthesis of periodic control systems for various engineering and mechanical problems are strongly related to the well known matrix equations, i.e., Lyapunov or Riccati equations. This paper presents the iterative methods for solving large-scale sparse projected discrete-time periodic Lyapunov equations which arise in periodic state feedback control problems and in model reduction of periodic descriptor systems. We extend the alternating direction implicit method and the Smith method to such equations and discuss their applications to the model reduction procedure for periodic descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.