We present an event-triggered observer design for linear time-invariant systems, where the measured output is sent to the observer only when a triggering condition is satisfied. We proceed by emulation and we first construct a continuous-time Luenberger observer. We then propose a dynamic rule to trigger transmissions, which only depends on the plant output and an auxiliary scalar state variable. The overall system is modeled as a hybrid system, for which a jump corresponds to an output transmission. We show that the proposed event-triggered observer guarantees global practical asymptotic stability for the estimation error dynamics. Moreover, under mild boundedness conditions on the plant state and its input, we prove that there exists a uniform strictly positive minimum inter-event time between any two consecutive transmissions, guaranteeing that the system does not exhibit Zeno solutions. Finally, the proposed approach is applied to a numerical case study of a lithium-ion battery.

中文翻译：

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线性系统的事件触发观察器设计

我们提出了一种用于线性时不变系统的事件触发观察器设计，其中仅在满足触发条件时才将测量输出发送给观察器。我们通过仿真进行，我们首先构建了一个连续时间 Luenberger 观测器。然后我们提出了一个动态规则来触发传输，该规则仅取决于设备输出和辅助标量状态变量。整个系统被建模为混合动力系统，其中跳跃对应于输出传输。我们表明，所提出的事件触发观察器保证了估计误差动态的全局实际渐近稳定性。此外，在植物状态及其输入的温和有界条件下，我们证明在任何两个连续传输之间存在统一的严格正最小事件间时间，保证系统不展示 Zeno 解决方案。最后，将所提出的方法应用于锂离子电池的数值案例研究。