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Exponential stabilization of conservation systems with interior disturbance. (English) Zbl 1330.93210
Summary: 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.

##### MSC:
 93D21 Adaptive or robust stabilization 93B12 Variable structure systems 93B52 Feedback control 47H05 Monotone operators and generalizations
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