A novel extended precise integration method based on Fourier series expansion for the H-2-norm of linear time-varying periodic systems
A novel extended precise integration method based on Fourier series expansion for the H-2-norm of linear time-varying periodic systems
复制标题
一种基于傅里叶级数展开的线性时变周期系统H-2范数的新型扩展精确积分方法
DOI：
10.1080/00207179.2016.1148271
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发表时间：
2016
影响因子：
2.1
通讯作者：
Wu Zhi-Gang
中科院分区：
文献类型：
--
作者：
Tan Shu-Jun;Peng Hai-Jun;Zhou Wen-Ya;Wu Zhi-Gang
提出了一种利用周期Lyapunov微分方程(PLDE)计算线性时变周期(LTP)系统H2范数的可靠算法。基于傅里叶级数展开的扩展精细积分方法，充分利用LTP系统的周期性，有效地计算了与PLDE相关的LTP系统的转移矩阵，避免了在每个子区间计算矩阵指数及其相关积分的耗时工作。然后，利用转移矩阵的分块形式，推导出了一种高精度、高效率的PLDE算法。因此，可以通过求解一个简单的一阶常微分方程组来计算H2范数。最后，给出了两个数值算例，并与其他算法进行了比较，验证了该算法的数值精度和效率。
A new reliable algorithm for computing the H2-norm of linear time-varying periodic (LTP) systems via the periodic Lyapunov differential equation (PLDE) is proposed. By taking full advantage of the periodicity, the transition matrix of the underlying LTP system associated with the PLDE is effectively computed by developing a novel extended precise integration method based on Fourier series expansion, where the time-consuming work for the computation of the matrix exponential and its related integrals in every sub-interval is avoided. Then, a highly accurate and efficient algorithm for the PLDE is derived using the block form of the transition matrix. Thus, the H2-norm is evaluated by solving a simple first-order ordinary differential equation. Finally, two numerical examples are presented and compared with other algorithms to verify the numerical accuracy and efficiency of the proposed algorithm.