Boundary observer design for a system of ODEs in cascade with hyperbolic PDEs is studied. An infinite dimensional observer is used to solve the state estimation problem. The interconnection of the observer and the system is written in estimation error coordinates and analyzed as an abstract dynamical system. The design of the observer is performed to achieve global exponential stability of the estimation error with respect to a suitable norm and with a tunable convergence rate. Sufficient conditions in the form matrix inequalities are given for the design of the observer. The effectiveness of the approach is shown in a numerical example.

中文翻译：

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级联ODE的边界观测器设计—双曲PDE系统：矩阵不等式方法

研究了双曲PDE级联的ODE系统的边界观测器设计。无限维观测器用于解决状态估计问题。观察者与系统的互连被写入估计误差坐标中，并作为抽象的动力学系统进行分析。执行观察者的设计，以实现估计误差相对于适当范数和可调收敛率的全局指数稳定性。形式矩阵不等式的充分条件为观察者的设计提供了条件。数值示例显示了该方法的有效性。