Stabilisation of non-diagonal infinite-dimensional systems with delay boundary control

Abstract

Here we deal with the stabilisation problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into two components: an unstable and a stable one. To stabilise the unstable part of the system, we connect, for the first time in the literature, the famous backstepping control design technique with the direct-proportional control design. More precisely, we construct a proportional open-loop stabiliser, then, by means of the Artstein transformation we close the loop. At the end of the paper, an example is provided in order to illustrate the acquired results.

Keywords:

• Projection
• boundary delay feedback control
• stabilisation
• backstepping control design
• direct-proportional control design

Acknowledgments

Thanks are due to the Anonymous Referees for their precious comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by a grant of the Romanian Ministry of Research and Innovation, CNCS – UEFISCDI, project number PN-III-P1-1.1-TE-2019-0348, within PNCDI III.