This paper considers a scalar continuous-time linear time-invariant system, whose feedback signal is transmitted through a communication network. Such a network has only finite bit rate and suffers from transmission delay which is characterized by both lower and upper delay bounds. The concerned system implements event-triggering strategies, i.e., only when certain events are triggered, the system samples and transmits feedback signals. This paper first derives some lower bounds on the feedback bit rate required to achieve the input-to-state stability under arbitrary event-triggering strategies. Then this paper proposes some constructive methods to design the event-triggering strategy and the controller, and can achieve the input-to-state stability at a bit rate being arbitrarily close to these obtained lower bit rate bounds. Moreover, this paper proves that the stabilizing bit rates under the proposed event-triggering strategies can be strictly lower than the stabilizing bit rate required by any time-triggering strategy. This bit rate superiority comes from the fact that under event triggering, the state information can be freely extracted from the receive time instants of feedback packets without consuming any bit rate. Simulations are done to demonstrate the bit rate superiority of the proposed event-triggering strategies.

中文翻译：

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稳定基于事件触发的标量连续时间 LTI 系统的必要且充分的比特率条件

本文考虑一个标量连续时间线性时不变系统，其反馈信号通过通信网络传输。这种网络只有有限的比特率，并且受到传输延迟的影响，传输延迟的特点是延迟上下界。相关系统执行事件触发策略，即只有当某些事件被触发时，系统才会采样并传输反馈信号。本文首先推导出在任意事件触发策略下实现输入到状态稳定性所需的反馈比特率的一些下限。然后本文提出了一些建设性的方法来设计事件触发策略和控制器，并且可以在任意接近这些获得的比特率下限的比特率下实现输入到状态的稳定性。而且，本文证明了所提出的事件触发策略下的稳定比特率可以严格低于任何时间触发策略所需的稳定比特率。这种比特率优势来自这样一个事实，即在事件触发下，状态信息可以从反馈数据包的接收时刻中自由提取，而不会消耗任何比特率。进行模拟以证明所提出的事件触发策略的比特率优势。状态信息可以从反馈包的接收时刻中自由提取，而不消耗任何比特率。进行模拟以证明所提出的事件触发策略的比特率优势。状态信息可以从反馈包的接收时刻中自由提取，而不消耗任何比特率。进行模拟以证明所提出的事件触发策略的比特率优势。