MIMO线性动力系统的H ~ 2-最优逼近
H2-optimal approximation of MIMO linear dynamical systems
摘要：
考虑了用一个次数小得多的多输入多输出（MIMO）$p\times m$有理传递函数$H(s)$逼近一个次数高的多输入多输出（MIMO）$p\times m$有理传递函数$H(s)$的问题，使得逼近误差的${\cal H}_2$范数最小.我们通过切向插值条件刻画了逼近误差的${\cal H}_2$范数的稳定点，并将这些结果推广到离散时间情形。我们分析是否合理的假设，低阶模型总是可以近似任意接近只施加一阶插值条件。最后，为了说明最小化问题的复杂性，我们分析了一个简单情况下的近似误差的${\cal H}_2$范数。
英文摘要：
We consider the problem of approximating a multiple-input multiple-output (MIMO) $p\times m$ rational transfer function $H(s)$ of high degree by another $p\times m$ rational transfer function $\hat H(s)$ of much smaller degree, so that the ${\cal H}_2$ norm of the approximation error is minimized. We characterize the stationary points of the ${\cal H}_2$ norm of the approximation error by tangential interpolation conditions and also extend these results to the discrete-time case. We analyze whether it is reasonable to assume that lower-order models can always be approximated arbitrarily closely by imposing only first-order interpolation conditions. Finally, we analyze the ${\cal H}_2$ norm of the approximation error for a simple case in order to illustrate the complexity of the minimization problem.
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