论文标题
研究开关最大线性系统稳定性的框架
Framework for Studying Stability of Switching Max-Plus Linear Systems
论文作者
论文摘要
我们提出了一个框架，用于研究以切换最大线性系统模型的离散事件系统的稳定性。在此框架中，我们提出了最大代数中通用离散事件系统的一组稳定性概念。然后，由于缺乏全局单调性和严格分析的伴随难度，我们显示了这些概念切换最大线性系统的等效性的丧失。这是放松动力学对最大锥体阳性不变性单调性的假设的动机。然后，当动力学仅限于此类锥体时，我们继续概括稳定性的概念。本文介绍的稳定分析方法是研究一般切换最大线性系统的稳定性的第一步。
We propose a framework for studying the stability of discrete-event systems modelled as switching max-plus linear systems. In this framework, we propose a set of notions of stability for generic discrete-event systems in the max-plus algebra. Then we show the loss of equivalence of these notions for switching max-plus linear systems due to the lack of global monotonicity and the accompanying difficulty in rigorous analysis. This serves as a motivation to relax the assumption on monotonicity of the dynamics to positive invariance of max-plus cones. Then we proceed to generalise the notions of stability when the dynamics is restricted to such cones. The stability analysis approach presented in this paper serves as a first step to study the stability of a general class of switching max-plus linear systems.
