This paper presents a novel method to compute the distance to instability for linear time-invariant delay systems with multiple delays, subjected to combined uncertainties on the system matrices and the delay parameters. The method is able to fully exploit structure and possible interdependencies between the uncertainties affecting the coefficient matrices, the property that realistic perturbations are real valued, and the structure of the delay equation. The resulting algorithm relies on a characterization in terms of the pseudospectral abscissa and on techniques from optimization over manifolds of matrices.

中文翻译：

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一种计算延迟和系统矩阵组合不确定性的结构化距离的新方法

本文提出了一种计算具有多个延迟的线性时不变延迟系统的不稳定距离的新方法，该系统受到系统矩阵和延迟参数的组合不确定性的影响。该方法能够充分利用影响系数矩阵的不确定性、现实扰动是实值的特性以及延迟方程的结构之间的结构和可能的相互依赖性。所得算法依赖于伪谱横坐标方面的表征和矩阵流形优化技术。