论文标题
Legendre近似产生的时间延迟系统的必要稳定条件
Necessary and sufficient stability condition for time-delay systems arising from Legendre approximation
论文作者
论文摘要
最近，已证明有足够的稳定性或不稳定性条件是必要的。这样，Gomez等人就已经开发出了一个显着和充分的条件。它作为对从Lyapunov矩阵发出的基质的正面确定性的简单测试。在本文中，提出了此结果的扩展。没有详细介绍，国家的统一离散化已被第一个Legendre多项式的预测所取代。像Gomez等人基于收敛参数一样，必要性以有限顺序获得，可以通过分析进行计算。与他们相比，通过依靠Legendre近似的快速收敛速率，确保稳定性降低的所需顺序。如示例部分所示，借助此重大修改，可以找到低订单和不稳定订单的稳定区域的稳定区域。
Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a simple test of positive definiteness of a matrix issued from the Lyapunov matrix. In this paper, an extension of this result is presented. Without going into details, the uniform discretization of the state has been replaced by projections on the first Legendre polynomials. Like Gomez et al., based on convergence arguments, the necessity is obtained in finite order, which can be calculated analytically. Compared to them, by relying on the fast convergence rate of Legendre approximation, the required order to ensure stability has been reduced. Thanks to this major modification, as shown in the example section, it is possible the find stable regions for low orders and unstable ones for even smaller orders.
