Exponential Stabilization of a Star-Shaped Thermoelastic Network System Based on the Extended State Observer With Time-Varying Gains

The boundary stabilization problem of a star-shaped type II thermoelastic system is considered, where there is a nonuniform bounded disturbance at the control end. A time-varying extended state observer is proposed to estimate and cancel the disturbance, thereby largely removing the uncertainties and simplifying the feedback control law design. The exponential stability is shown for the extended state observer, so are the well-posedness properties of the closed-loop system, all based on the linear operator semigroup theory. Finally, it is shown that the disturbances can be attenuated and the resulting closed-loop system can exponentially approach zero. Numerical simulations illustrate the effectiveness of the proposed control strategy.

Automated summary

This study addresses the boundary stabilization problem of a star-shaped type II thermoelastic system with a nonuniform bounded disturbance at the control end. A time-varying extended state observer is proposed to estimate and cancel the disturbance, greatly reducing uncertainties and facilitating feedback control law design. Exponential stability of the extended state observer and well-posedness properties of the closed-loop system are proven based on linear operator semigroup theory. It is also demonstrated that disturbances can be attenuated and the resulting closed-loop system can exponentially approach zero, with numerical simulations validating the effectiveness of the proposed control strategy.