Strong and weak output stabilisation for distributed bilinear systems

Abstract

This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain Ω. We give sufficient conditions for strong and weak output stabilisation. Also, the output stabilisation is discussed using a minimisation problem. Examples and simulations are given.

Keywords:

• Bilinear systems
• output stabilisation
• feedback controls
• decay estimate
• minimisation problem

Acknowledgments

The authors are grateful to both referees and the editor, for all useful comments and suggestions, which have greatly helped to improve the presentation of this paper.

Disclosure statement

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

Additional information

Funding

This work was supported by Académie Hassan II des Sciences et Techniques [630/2016].

Notes on contributors

Abderrahman Ait Aadi

Abderrahman Ait Aadi is a researcher at MACS Laboratory, University Moulay Ismail of Meknes, Morocco. He received his doctorate in Applied Mathematics (2019) at the Faculty of Sciences in Meknes. He wrote many papers in the area of systems theory and especially in optimal control and stabilisation of infinite dimensional systems.

El Hassan Zerrik

El Hassan Zerrik is a Professor at Moulay Ismail University of Meknes in Morocco. He was an assistant professor at the Faculty of Sciences of Meknes and a researcher at Perpignan University (France). He got his PhD degree in 1993, at Mohammed V University of Rabat, Morocco. Professor Zerrik wrote many papers and books in the area of systems theory and especially in regional control and analysis of infinite dimensional systems. Now he is the head of the research MACS Laboratory, at Moulay Ismail University of Meknes in Morocco.