时滞微分-代数方程可解性与稳定性的谱特征
Spectral Characterizations of Solvability and Stability for Delay Differential-Algebraic Equations
摘要：
分析了时滞微分代数方程线性定常系统的可解性和稳定性。行为的方法被施加到DDAE，以建立其可解性的谱条件方面的表征。最后，通过算例说明了基于特征值的动力系统指数稳定性分析方法只适用于一类特殊的非先进DDAE。在此基础上，提出了弱稳定性的概念，并研究了矩阵系数两两可换的DDAE系统的弱稳定性。
英文摘要：
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in terms of spectral conditions. Furthermore, examples are delivered to demonstrate that the eigenvalue-based approach to analyze the exponential stability of dynamical system is only valid for a special class of DDAEs, namely non-advanced. Then, a new concept of weak stability is proposed and studied for DDAEs whose matrix coefficients pairwise commute.
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