Stability analysis of sampled-data ODE–Schrödinger systems and its applications to output-feedback stabilization

In this paper, we are concerned with a sampled-data cascades system, which consists of finite-dimensional dynamics described by ordinary differential equation (ODE) and infinite-dimensional dynamics represented by a Schrödinger equation, based on a zero-order-holder (ZOH) measurement signal. The Schrödinger equation includes reaction and convection terms, and allows more general boundary conditions. Then, a small-gain approach is used to analyze the exponential stability of this hybrid system. This stability analysis is shown to be very useful in the design of sampled-data exponentially convergent observers and exponentially stable output-feedback controllers for some classes of ODE–Schrödinger cascaded system.