A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with Lyapunov-based analysis techniques for hybrid systems. In virtually all papers that use this framework, bounds in terms of the maximal allowable transmission interval (MATI) are provided to guarantee stability, and performance properties of the NCS. However, having only such a MATI condition is rather restrictive, and unrealistic in practice due to various network effects such as packet losses, leading to conservative bounds. In this article, we therefore consider an alternative condition on the communication instants to better capture the time-varying properties of the transmission intervals. In particular, we propose, in addition to the existence of a MATI, to also impose a bound on the average allowable transmission interval, expressed in terms of a reverse average dwell-time condition on the transmission intervals. We demonstrate by means of a novel Lyapunov-based analysis that stability of the NCS can still be guaranteed under this different condition on the transmission intervals, which can, in addition, lead to a significant improvement of the MATI. The strengths of these new results will be illustrated on a numerical example.

中文翻译：

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网络控制系统稳定性的平均允许传输间隔条件


网络控制系统 (NCS) 的流行设计框架是基于仿真的方法与基于李亚普诺夫的混合系统分析技术的结合。实际上，在所有使用该框架的论文中，都提供了最大允许传输间隔 (MATI) 方面的界限，以保证 NCS 的稳定性和性能特性。然而，由于诸如数据包丢失之类的各种网络效应，仅具有这样的 MATI 条件是相当有限制的，并且在实践中是不现实的，从而导致保守的界限。因此，在本文中，我们考虑了通信时刻的替代条件，以更好地捕获传输间隔的时变属性。特别是，我们建议，除了 MATI 的存在之外，还对平均允许传输间隔施加限制，以传输间隔上的反向平均停留时间条件来表示。我们通过一种新颖的基于 Lyapunov 的分析证明，在这种不同的传输间隔条件下，仍然可以保证 NCS 的稳定性，此外，这还可以导致 MATI 的显着改善。这些新结果的优点将通过数值示例进行说明。