Output feedback stabilisation of parallel coupled string equations with matched boundary disturbance

ABSTRACT

In this paper, we are concerned with boundary output feedback stabilisation of two parallel coupled string equations with matched external disturbance. By the method proposed by Feng and Guo in IEEE Transactions on Automatic Control [62(2017), pp. 3774–3787], we design a disturbance estimator first which is used to cancel the effect of disturbance in the feedback loop. The other part of output feedback controller is designed to make system stable. Then operator semigroup and Lyapunov function methods are adopted to prove that the closed-loop system admits a unique solution in state space, the solution of original system is asymptotically stable and one of the disturbance estimator system is bounded. Finally, numerical simulations are presented to validate the theoretical results.

KEYWORDS:

• Parallel coupled string equations
• boundary control
• disturbance estimator
• output feedback

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [ 61603226].