General Solution to Standard H∞Control Problems for a Class of Infinite-dimensional Systems
General Solution to Standard H∞Control Problems for a Class of Infinite-dimensional Systems
复制标题
标准 H 的通解
DOI：
10.1109/cdc.2005.1582531
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Y. Yamamoto
中科院分区：
文献类型：
--
作者：
K. Kashima;Y. Yamamoto
本文研究传递函数可表示为有理传递矩阵和标量（可能是无理的）内函数的级联的无限维系统的H∞控制问题。这类系统非常适合于描述实际中的许多控制问题，当权函数是有理数且对象至多有100个不稳定模态时。我们表明，这个问题可以减少到两个（矩阵值）Riccati方程和额外的秩条件。此外，所得到的控制器结构的特点是完全的内函数和控制器的有限维部分。最后给出了一个数值例子来说明结果。
This paper considers H∞-control of infinite-dimensional systems whose transfer functions are expressible as the cascade connection of a rational transfer matrix and a scalar (possibly irrational) inner function. This class of systems is very suitable for describing many control problems in practice, when weighting functions are rational and plants have at most finitely many unstable modes. We show that this problem can be reduced to two (matrix-valued) Riccati equations and additional rank conditions. Furthermore, the obtained controller structure is completely characterized by the inner function and controllers for the finite-dimensional part. A numerical example is given to illustrate the result.