In this paper, we analyse the impact of delayed event detection on the stability of a 2-mode planar hybrid automata. We consider hybrid automata with a unique equilibrium point for all the modes, and we find the maximum delay that preserves stability of that equilibrium point. We also show for the class of hybrid automata treated that the instability of the equilibrium point for the equivalent hybrid automaton with delay in the transitions is equivalent to the existence of a closed orbit in the hybrid state space, a result that is inspired by the Joint Spectral Radius theorem. This leads to an algorithm for computing the maximum stable delay exactly. Other potential applications of our technique include co-simulation, networked control systems and delayed controlled switching with a state feedback control.

中文翻译：

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延迟事件检测下平面切换系统的稳定性

在本文中，我们分析了延迟事件检测对 2 模式平面混合自动机稳定性的影响。我们考虑所有模式都具有唯一平衡点的混合自动机，我们找到了保持该平衡点稳定性的最大延迟。我们还表明，对于处理过的混合自动机类，具有转换延迟的等效混合自动机的平衡点的不稳定性等效于混合状态空间中闭合轨道的存在，这是受联合启发的结果谱半径定理。这导致了一种用于精确计算最大稳定延迟的算法。我们技术的其他潜在应用包括协同仿真、网络控制系统和具有状态反馈控制的延迟控制切换。