Exponential stabilization of conservation systems with interior disturbance

In this paper, we consider the stabilization problem of the conservation systems with interior disturbance. Employing the idea of sliding-mode control, we design a nonlinear distributed feedback controller. We prove the solvability of the resulted closed-loop system by the maximal monotone operator theory. Further we prove the exponential stability of the closed-loop system. In particular, we prove that the requirement of a classical solution in the Lyapunov approach is unnecessary.