This paper deals with the exponential stability analysis of decentralized, sampled-data, Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency, which translates to asynchrony between sensors and actuators. Additionally, asynchrony may be induced by delays between the sampling instants and actuation update instants as relevant in a networked context. The decentralized, asynchronous LTI system is represented as the feedback interconnection of a continuous-time LTI system operator and an operator that captures the effects of asynchrony induced by sampling and delay. By characterizing the properties of the operators using small-gain type Integral Quadratic Constraints (IQC), we provide criteria for exponential stability of the asynchronous, decentralized LTI state-space models. The approach provided in this paper considers two scenarios, namely the ‘large-delay’ case and the ‘small-delay’ case where the delays are larger and smaller than the sampling interval, respectively. The effectiveness of the proposed results is corroborated by a numerical example.

本文涉及分散的，采样数据，线性时不变的指数稳定性分析（LTI）控制系统，带有异步传感器和执行器。我们考虑在分散设置中的每个控制器都有其自己的采样和启动频率的情况，这会转化为传感器和执行器之间的异步。另外，异步可能由网络环境中相关的采样时刻和致动更新时刻之间的延迟引起。分散的异步LTI系统表示为连续时间LTI系统运营商和捕获采样和延迟引起的异步影响的运营商的反馈互连。通过使用小增益类型积分二次约束（IQC）表征算子的属性，我们为异步，分散LTI状态空间模型的指数稳定性提供了标准。本文提供的方法考虑了两种情况，即延迟分别大于和小于采样间隔的“大延迟”情况和“小延迟”情况。数值例子证实了所提出结果的有效性。