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Algorithms for fast calculation of spectral abscissa for retarded time-delay systems with delay-dependent coefficients ?

机译:用于延迟依赖系数的延迟时间延迟系统的快速计算算法

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Time-delay systems with delay-dependent coefficients arise from different disciplines, but methods and algorithms for stability analysis of this kind of systems are very few compared with the intensive ones for time-delay systems with delay-free coefficients. This paper presents three algorithms for calculating the spectral abscissa of these time-delay systems with the delay as a parameter, an index that determines the stability and the decaying rate of the systems. The key step of the proposed algorithms is the use of parametric continuation method to calculate the real part branches by solving initial value problems of an ordinary differential equation derived from the characteristic function, where the initial values of the initial value problems are chosen as the rightmost characteristic roots, or the second rightmost characteristic roots, and so on, and they are calculated by using the integration-based-stability-test method. The algorithms are particularly effective when the delay interval is short.
机译:具有延迟相关系数的时滞系统来自不同的学科,但是与具有延迟系数的时间延迟系统的密集系统相比,这种系统的稳定性分析的方法和算法非常少。本文呈现了三种算法,用于计算这些时滞系统的频率横坐标,延迟作为参数,该索引确定系统的稳定性和衰减率。所提出的算法的关键步骤是使用参数连续方法来通过求解从特征函数导出的常微分方程的初始值问题来计算实部分支,其中初始值问题的初始值被选为右侧特征根部,或第二最右边的特征根,等等,通过使用基于集成的稳定性测试方法来计算它们。当延迟间隔短时,算法特别有效。

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