论文标题
时间延迟系统的伪造横坐标计算的预测 - 矫正器类型
A Predictor-Corrector Type Algorithm for the Pseudospectral Abscissa Computation of Time-Delay Systems
论文作者
论文摘要
线性时变系统的伪谱是当系统矩阵受到所有可能的扰动与给定上限的所有可能的扰动时，由特征方程的所有根组成的复合平面中的集合。伪横肌的定义是伪谱中特征根的最大实际部分，因此，从强大的稳定性角度来看，它是重要的。在本文中，我们提出了一种准确的方法，用于计算具有离散延迟的智障延迟微分方程的伪横梁。我们的方法基于伪谱与适当定义的复杂函数的级别集之间的连接。计算分两个步骤进行。在预测步骤中，基于特征矩阵的合理近似和一分配算法的应用，获得了伪腹部的近似值。该二进制算法中的每个步骤都依赖于检查复合矩阵的假想轴特征值的存在，类似于延迟自由情况。在校正步骤中，通过求解一组表征伪镜轮廓中极端点的非线性方程，将近似伪横梁校正为任何给定精度。
The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound. The pseudospectral abscissa is defined as the maximum real part of the characteristic roots in the pseudospectrum and, therefore, it is for instance important from a robust stability point of view. In this paper we present an accurate method for the computation of the pseudospectral abscissa of retarded delay differential equations with discrete pointwise delays. Our approach is based on the connections between the pseudospectrum and the level sets of an appropriately defined complex function. The computation is done in two steps. In the prediction step, an approximation of the pseudospectral abscissa is obtained based on a rational approximation of the characteristic matrix and the application of a bisection algorithm. Each step in this bisection algorithm relies on checking the presence of the imaginary axis eigenvalues of a complex matrix, similar to the delay free case. In the corrector step, the approximate pseudospectral abscissa is corrected to any given accuracy, by solving a set of nonlinear equations that characterize extreme points in the pseudospectrum contours.
