Sliding mode control to the stabilization of a linear 2×2 hyperbolic system with boundary input disturbance

In this paper, sliding mode control approach is used to stabilize a 2×2 system of first-order linear hyperbolic PDEs subject to boundary input disturbance. Disturbance rejection is achieved, and with the designed first-order sliding mode controller, the resulting closed-loop system admits a unique (mild) solution without chattering. Convergence to the chosen infinite-dimensional sliding surface of state trajectories takes place in a finite time. Then on the sliding surface, the system is exponentially stable with a decay rate depending on the spatially varying system coefficients. A simulation example is presented to illustrate the effectiveness and performance of sliding mode control method.