Observer design for linear systems with aperiodic sampled-data measurements is addressed. To solve this problem, a novel hybrid observer is designed. The main peculiarity of the proposed observer consists of the use two output injection terms, one acting at the sampling instants and one providing an intersample injection. The error dynamics are augmented with a timer variable triggering the arrival of a new measurement and analyzed via hybrid system tools. Using Lyapunov theory, sufficient conditions for the convergence of the observer are provided. Relying on those conditions, an optimal LMI-based design is proposed for the observer gains. The effectiveness of the approach is illustrated in an example.

中文翻译：

---

线性非周期性采样数据系统的观测器设计：一种混合系统方法

解决了具有非周期性采样数据测量的线性系统的观测器设计。为了解决这个问题，设计了一种新型的混合观测器。提出的观察者的主要特点是使用两个输出注入项，一个在采样时刻起作用，一个提供采样间注入。借助触发新测量值的计时器变量来增强错误动态，并通过混合系统工具进行分析。使用李雅普诺夫理论，为观察者的收敛提供了充分的条件。依靠这些条件，为观察者的增益提出了基于LMI的最佳设计。示例中说明了该方法的有效性。