Stability Analysis of a ${\text{2}}\times {\text{2}}$ Linear Hyperbolic System With a Sampled-Data Controller via Backstepping Method and Looped-Functionals

This paper is concerned with the global exponential stability of a 2 X 2 linear hyperbolic system with a sampled-data boundary feedback control designed by means of the backstepping method for a nominal continuous input. We show that there exists a sufficiently small intersampling time (that encompasses both periodic and aperiodic sampling) for which the global exponential stability of the closed-loop system is guaranteed. In addition, we provide easily tractable sufficient stability conditions that can be used to find an upper bound of the maximum intersampling time. The results rely on the combination of the Lyapunov method and looped-functionals. The effectiveness of the proposed results is illustrated with a numerical example.