Computation of the induced norm from L2 to L∞ in SISO sampled-data systems: Discretization approach with convergence rate analysis
Computation of the induced norm from L2 to L∞ in SISO sampled-data systems: Discretization approach with convergence rate analysis
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SISO 采样数据系统中从 L2 到 L∞ 的归纳范数的计算：具有收敛速度分析的离散化方法
DOI：
10.1109/cdc.2015.7402463
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
T. Hagiwara
中科院分区：
文献类型：
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作者：
Jung Hoon Kim;T. Hagiwara
针对单输入单输出（SISO）线性时不变（LTI）采样系统，给出了一种计算L2到L∞诱导范数的离散化方法.本文首先对SISO LTI采样系统的L2到L∞的诱导范数进行提升处理，然后进一步应用快速提升的关键思想，将采样区间[0，h）划分为M个等宽子区间.这样的想法使我们能够开发两种方法来计算诱导范数网格和分段常数近似。这些方法导致近似等效的离散化方法的广义植物，可以用于容易地计算上界和下界的诱导范数连同相关的收敛速度的推导。更准确地说，它表明，逼近误差收敛到0的速度为1/100 M和1/M的网格和分段常数逼近方法，分别。
This paper provides a discretization method for computing the induced norm from L2 to L∞ in single-input/ single-output (SISO) linear time-invariant (LTI) sampled-data systems. We first follow the lifting-based treatment for the induced norm from L2 to L∞ of SISO LTI sampled-data systems, but further apply the key idea of fast-lifting, by which the sampling interval [0, h) is divided into M subintervals with an equal width. Such an idea allows us to develop two methods for computing the induced norm with gridding and piecewise constant approximations. These methods leads to approximately equivalent discretization methods of the generalized plant that can be used for readily computing upper and lower bounds of the induced norm together with the derivation of the associated convergence rates. More precisely, it is shown that the approximation error converges to 0 at the rate of 1/√M and 1/M in the gridding and piecewise constant approximation methods, respectively.
用于采样数据系统分析的改进的快速采样/快速保持近似
DOI：
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发表时间：
2008
期刊：
European Journal of Control Vol.14, No.4
影响因子：
--
作者：
T;Hagiwara;T. Hagiwara and R. Mori;T. Hagiwara and H. Umeda
通讯作者：
T. Hagiwara and H. Umeda
DOI：
10.1109/9.286247
发表时间：
1994-04
期刊：
IEEE Trans. Autom. Control.
影响因子：
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作者：
Y. Yamamoto
通讯作者：
Y. Yamamoto