Output feedback stabilisation for a cascaded wave PDE-ODE system subject to boundary control matched disturbance

ABSTRACT

In this paper, we consider output feedback stabilisation for a wave PDE-ODE system with Dirichlet boundary interconnection and external disturbance flowing the control end. We first design a variable structure unknown input type state observer which is shown to be exponentially convergent. Then, we estimate the disturbance in terms of the estimated state, an idea from active disturbance rejection control. These enable us to design an observer-based output feedback stabilising control to this uncertain PDE-ODE system.

Keywords:

• Output feedback
• stabilisation
• wave PDE-ODE system
• backstepping
• active disturbance rejection control
• disturbance

AMS subject classifications:

• 35L05
• 93B52
• 37L15
• 93D15
• 93B51

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was carried out with the support of the National Natural Science Foundation of China, the National Basic Research Program of China [Grant Number 2011CB808002], and the National Research Foundation of South Africa.