Analysis and Control of Time Delayed Systems via the Lambert W Function ?
Analysis and Control of Time Delayed Systems via the Lambert W Function ?
复制标题
通过兰伯特 W 函数分析和控制时滞系统？
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
S. Yi
中科院分区：
文献类型：
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作者：
S. Yi
本文综述了作者近年来利用矩阵LambertW函数求解时滞微分方程组的研究成果，及其在时滞系统分析与控制中的应用。该解决方案的形式的一个无限系列的模式写在矩阵兰伯特W功能。这个解决方案是解析的参数，系数和延迟时间，系统，和每个本征值在无限本征谱的Lambert W函数的分支来区分。这使得扩展的方法系统的常微分方程系统的延迟微分方程。这些包括稳定性分析，可控性和可观性，以及方法的特征值分配。
This paper summarizes recent research results by the authors for the analytical solution to systems of delay differential equations using the matrix Lambert W function, and its applications to analysis and control of time-delay systems. The solution has the form of an infinite series of modes written in terms of the matrix Lambert W function. This solution is analytical in terms of the parameters, coefficients and delay time, of the system, and each eigenvalue in the infinite eigenspectrum is distinguished in terms of the branches of the Lambert W function. This enables extension of methods for systems of ordinary differential equations to systems of delay differential equations. These include stability analysis, controllability and observability, as well as methods for eigenvalue assignment.