Output feedback stabilisation of a tree-shaped network of vibrating strings with non-collocated observation

摘要

In this article, the authors consider the simple tree-shaped network of strings with non-collocated observation. Suppose that the network consists of three strings and the displacements of these strings are continuous at the common vertex. The sensors and actuators are required to be set at different vertices. We propose an observer-based output feedback controller to stabilise this network. The exponential stability of the closed-loop network is obtained based on the Riesz basis approach together with estimates of the spectral distribution. Finally, a numerical simulation is given to support these results.