论文标题
计算时间延迟系统的H-内在规范
Computing H-infinity Norms of Time-Delay Systems
论文作者
论文摘要
在本文中，我们考虑了具有离散点状状态延迟的延迟时间延迟系统的H-赋值范围的计算。众所周知，在有限的尺寸情况下，系统的h-触发性是使用传递函数的奇异值与哈密顿矩阵的假想轴特征值之间的连接计算的。我们显示了时间延迟系统传输函数的奇异值与无限尺寸运算符$ \ MATHCAL {l} _配的无限轴特征值的单数值。使用光谱方法，该线性操作员用矩阵近似。时间延迟系统的近似h-----使用该矩阵的假想特征值与时间延迟系统的有限维近似值的奇异值之间的连接计算。最后，通过求解一组方程来纠正近似结果，这些方程是从$ \ Mathcal {l}_ξ$作为有限维度非线性特征值问题的特征值问题的重新印度获得的。
In this paper we consider the computation of H-infinity norm of retarded time-delay systems with discrete pointwise state delays. It is well known that in the finite dimensional case H-infinity norm of a system is computed using the connection between the singular values of the transfer function and the imaginary axis eigenvalues of an Hamiltonian matrix. We show a similar connection between the singular values of a transfer function of a time-delay system and the imaginary axis eigenvalues of an infinite dimensional operator $\mathcal{L}_ξ$. Using spectral methods, this linear operator is approximated with a matrix. The approximate H-infinity norm of the time-delay system is calculated using the connection between the imaginary eigenvalues of this matrix and the singular values of a finite dimensional approximation of the time-delay system. Finally the approximate results are corrected by solving a set of equations which are obtained from the reformulation of the eigenvalue problem for $\mathcal{L}_ξ$ as a finite dimensional nonlinear eigenvalue problem.
