On the finite-time stabilization of some hyperbolic control systems by boundary feedback laws: Lyapunov approach

This paper discusses the finite-time stabilization of some linear hyperbolic partial differential equations by persistently exciting boundary feedbacks. The construction of stabilizing feedbacks is based on Lyapunov approach. A particular attention is paid to transport and wave control systems. The obtained results are used to solve two problems: the first one is finite-time stability of the SMB chromatography while the second application is the finite-time controllers of two strings connected by point mass.