The stability analysis for nonlinear differential-algebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a small-gain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory.

中文翻译：

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非线性微分代数系统的可加性稳定性

非线性微分代数系统的稳定性分析是使用经典控制理论中的工具进行的。通过Lyapunov Direct方法建立了依赖于矩阵不等式的充分稳定性条件。另外，将微分代数系统作为纯微分系统和代数系统的反馈互连的新颖解释，可以将稳定性分析降低到小增益状态。对受约束的机械系统，一类Lipschitz微分代数系统和一个学术实例的稳定性进行了研究，以说明该理论。