Sampled-data Boundary Observer Design for One-Dimensional ODE-Schrödinger Cascade System

In this paper, we are concerned with the sampled-data hybrid systems, described by a linear ordinary differential equation(ODE), and the partial differential equation(PDE) represented by a Schrödinger equation. We propose a small-gain method to analyse the exponential stability of this dynamical hybrid systems. This stability result proves to be useful in designing sampled-output exponentially convergent observers for systems that are represented by an ODE-PDE cascade. An illustration example is presented to confirm the effectiveness of the proposed exponential observer.