A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix Equations
A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix Equations
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DOI：
10.1007/s00034-014-9842-1
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
M. Hajarian
中科院分区：
文献类型：
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作者：
M. Hajarian
线性周期控制系统的分析与设计与离散周期矩阵方程密切相关。本文给出了求解一般耦合周期矩阵方程{A_1，I X_IB_1，I+C_1，I X_I+1 D_1，I=E_1，I，\A_2，I X_IB_2，I X_IB_2，I+C_2，I X_I+1D_2，I=E_2，I，I，~I~I=1，2，3，…的迭代算法。A 1，I X I B 1，I+C 1，I X I+1 D 1，I=E 1，I，A 2，I X I B 2，I+C 2，I X I+1 D 2，I=E 2，I，对于I=1，2，3，…。通过证明算法的一些性质，我们证明了在没有舍入误差的情况下，周期矩阵方程的解群可以在有限次迭代内得到。数值算例表明了该算法的有效性和准确性。
Abstract Analysis and design of linear periodic control systems are closely related to the discrete-time periodic matrix equations. In this paper, we propose an iterative algorithm based on the conjugate gradient method on the normal equations (CGNE) for finding the solution group of the general coupled periodic matrix equations {A_ 1, i X_iB_ 1, i+ C_ 1, i X_ i+ 1 D_ 1, i= E_ 1, i,\A_ 2, i X_iB_ 2, i+ C_ 2, i X_ i+ 1 D_ 2, i= E_ 2, i,.~~~ for~~~ i= 1, 2, 3, .... A 1, i X i B 1, i+ C 1, i X i+ 1 D 1, i= E 1, i, A 2, i X i B 2, i+ C 2, i X i+ 1 D 2, i= E 2, i, for i= 1, 2, 3,…. By proving some properties of the algorithm, we show that the solution group of the periodic matrix equations can be obtained within a finite number of iterations in the absence of roundoff errors. Numerical examples are given to illustrate the efficiency and accuracy of the proposed algorithm.