论文标题
具有代数约束的非线性时间延迟系统的隐式函数定理
Implicit function theorem for nonlinear time-delay systems with algebraic constraints
论文作者
论文摘要
在本说明中，我们将讨论众所周知的隐式函数定理的概括。我们表明，后一个问题与时间延迟系统的坐标的生物术变化密切相关。提出了一种迭代算法来检查条件并构建所提出的隐式函数定理的坐标的所需的bicausal变化。此外，我们表明我们的结果可以应用于延迟的差异代数方程（DDAE），以减少其指数并获取解决方案。给出了一些数值示例来说明我们的结果。
In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates of time-delay systems. An iterative algorithm is proposed to check the conditions and to construct the desired bicausal change of coordinates for the proposed implicit function theorem. Moreover, we show that our results can be applied to delayed differential-algebraic equations (DDAEs) to reduce their indices and to get their solutions. Some numerical examples are given to illustrate our results.
