Analysis and computation of stability exponents for port-Hamiltonian delay differential-algebraic equations (A02)

延迟微分代数方程（DDAE）出现在各种应用中，包括流量控制，生物系统和电力网络。在许多应用中，通过端口-哈密尔顿（pH）DDAE模型的模型层次来公式化DDAE是有利的。我们将研究此类pHDDAE的存在性、唯一性和敏感性，特别是那些子系统互连延迟的pHDDAE。我们将推导出变分公式，并研究由此产生的运营商pH DDAE相对于时空离散化和控制。特别是，我们将推导出模型简化技术和方法，用于估计pHDDAE的稳定区域。

Delay differential-algebraic equations (DDAEs) arise in a variety of applications including flow control, biological systems, and power networks. In many of the applications it is advantageous to formulate the DDAEs via a model hierarchy of port-Hamiltonian (pH) DDAE models. We will study existence, uniqueness and sensitivity for such pHDDAEs, in particular those where the interconnection of subsystems is delayed. We will derive vari-ational formulations and study the resulting operator pH DDAEs with respect to space-time discretization and control. In particular we will derive model reduction techniques and methods for the estimation of stability regions for pHDDAEs.