Abstract In this paper, we investigate differential–algebraic equations (DAEs) subject to stochastic perturbations. We introduce the index- ν concept and establish a formula of solution for these equations. After that the stability is studied by using the method of Lyapunov functions. Finally, the robust stability of DAEs with respect to stochastic perturbations is considered. Formulas of the stability radii are derived. An example is given to illustrate the obtained results.

中文翻译：

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微分代数方程关于随机扰动的稳定半径

摘要 在本文中，我们研究了受随机扰动影响的微分代数方程 (DAE)。我们引入了指数-ν 的概念并建立了这些方程的解公式。然后利用Lyapunov函数的方法研究稳定性。最后，考虑了 DAE 相对于随机扰动的稳健稳定性。推导出稳定半径的公式。给出一个例子来说明得到的结果。