In this paper, we develop a stability theory for implicit dynamic equations which is a general form of differential-algebraic equations and implicit difference equations. We derive some results about robust stability of these equations subjected to Lipschitz perturbations. After that the so-called Bohl–Perron type stability theorems, which are known in the literature for regular explicit difference equations, are extended for implicit dynamic equations. Finally, the notion of Bohl exponent is introduced and we characterise the relation between the exponential stability and the Bohl exponent. Then, it is investigated that how the Bohl exponent with respect to dynamic perturbations and two-side perturbations depends on the system data.

在本文中，我们开发了隐式动力学方程的稳定性理论，它是微分代数方程和隐式差分方程的一般形式。我们推导出了一些关于这些方程在 Lipschitz 扰动下的鲁棒稳定性的结果。之后，所谓的 Bohl-Perron 型稳定性定理（在文献中已知用于正则显式差分方程）被扩展到隐式动态方程。最后，介绍了 Bohl 指数的概念，我们刻画了指数稳定性和 Bohl 指数之间的关系。然后，研究了关于动态扰动和两侧扰动的 Bohl 指数如何依赖于系统数据。