Stabilization for a Hybrid System of Elasticity with Boundary Disturbances

The paper deals with a boundary feedback stabilization problem of a hybrid system with disturbances, which is clamped at one end and linked to a rigid body at the other end. The active disturbance rejection control approach is adopted in investigation. State observers are first designed to estimate disturbances, and then boundary feedback controllers are proposed to cancel the disturbances. Moreover, under different assumptions of time varying high gain functions, the asymptotical stability and the exponential stability of the closed-loop system are proved by the Lyapunov function approach. Finally, numerical simulations are presented to validate the theoretical conclusions.