Sliding Mode Control to Stabilization of a Tip-Force Destabilized Shear Beam Subject to Boundary Control Matched Disturbance

In this paper, we are concerned with the boundary stabilization of a one-dimensional tip-force destabilized shear beam equation subject to boundary control matched disturbance. We use the sliding mode control (SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system is proved and the “reaching condition” is obtained.

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