Abstract

We prove theorems on the Lyapunov stability, asymptotic stability, and instability of the equilibrium position of time-varying semilinear differential-algebraic equations (DAEs) as well as theorems about the asymptotic (complete) stability of these equations. As an example of applying the theorems on the global solvability of time-varying semilinear DAEs proved in the first part of this paper, we study a mathematical model of some electrical circuit.

中文翻译：

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时变半线性微分代数方程的整体可解性，解的有界性和稳定性。II

摘要

我们证明了时变半线性微分代数方程（DAE）的Lyapunov稳定性，渐近稳定性和平衡位置的不稳定性定理，以及这些方程的渐近（完全）稳定性定理。作为将定理应用到本文第一部分中证明的时变半线性DAE的整体可解性的一个例子，我们研究了一些电路的数学模型。