论文标题
时间延迟系统的H-赋值标准的表征和计算
Characterization and computation of H-infinity norms for time-delay systems
论文作者
论文摘要
我们考虑了一类时间延迟系统的H-赋值规范的表征和计算。众所周知，在有限的情况下，可以使用相应的奇异值曲线与汉密尔顿矩阵的假想轴特征值之间的连接来计算传递函数的H-赋值标准，从而导致既定水平集方法。我们显示了时间延迟系统的传输函数与无限尺寸线性运算符$ \ MATHCAL {l}_ξ^n $的假想轴特征值之间的类似连接。基于此结果，我们提出了一种用于计算H-依赖性规范的预测 - 校正算法。在预测步骤中，该问题的有限维近似是由操作员$ \ Mathcal {l}_松身分的频谱离散化引起的，以及适应有限维系统的算法，允许获得时间固定系统传输功能的H-触发函数的近似值。在下一步中，通过求解一组非线性方程式，将近似结果纠正到所需的准确性，这些方程是根据线性无限二维操作员$ \ MATHCAL {l} _配{l}_ξ^n $作为有限的非线性尺寸的非线性dimential dimential dimential dimens dimensional eigenear eigenvalue问题而获得的。这些方程可以解释为奇异值图中峰值的特征。预测变体中离散化的影响是充分表征的，并讨论了离散点数量的选择。本文以数值示例和广泛基准测试结果的介绍结束。
We consider the characterization and computation of H-infinity norms for a class of time-delay systems. It is well known that in the finite dimensional case the H-infinity norm of a transfer function can be computed using the connections between the corresponding singular value curves and the imaginary axis eigenvalues of a Hamiltonian matrix, leading to the established level set methods. We show a similar connection between the transfer function of a time-delay system and the imaginary axis eigenvalues of an infinite dimensional linear operator $\mathcal{L}_ξ^N$. Based on this result, we propose a predictor-corrector algorithm for the computation of the H-infinity norm. In the prediction step, a finite-dimensional approximation of the problem, induced by a spectral discretization of the operator $\mathcal{L}_ξ$, and an adaptation of the algorithms for finite-dimensional systems, allow to obtain an approximation of the H-infinity norm of the transfer function of the time-delay system. In the next step the approximate results are corrected to the desired accuracy by solving a set of nonlinear equations which are obtained from the reformulation of the eigenvalue problem for the linear infinite-dimensional operator $\mathcal{L}_ξ^N$ as a finite dimensional nonlinear eigenvalue problem. These equations can be interpreted as characterizations of peak values in the singular value plot. The effects of the discretization in the predictor step are fully characterized and the choice of the number of discretization points is discussed. The paper concludes with a numerical example and the presentation of the results of extensive benchmarking.
