Stabilisation of a thermo-elastic system under nonuniformly bounded disturbances in the boundary input

ABSTRACT

We consider the exponential stabilisation for a thermo-elastic system of type II with nonuniformly bounded external disturbances in the boundary control. We begin with finding feedback controls for the system without disturbances by Lyapunov function approach. Then, based on the resulting feedback control, we give new dynamic feedback control laws that make the system exponentially stable by tracking disturbances exponentially through a time-varying high gain observer. We apply the linear operator semi-group theory to prove the well-posedness of the resulting closed system. Finally, we prove that the solution of the closed-loop system can approach zero polynomially or exponentially by the Lyapunov function approach.

KEYWORDS:

• Thermo-elastic system
• disturbance rejection
• feedback control
• exponential stability
• polynomial stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the Natural Science Foundation of China [grant number NSFC-61174080], [grant number 61573252], [grant number 61503275].