Robust H_∞ controller design for uncertain 2D continuous systems with interval time-varying delays

ABSTRACT

The design of delay-dependent robust $H_{\mathrm{\infty }}$ controllers is solved here for a class of uncertain 2D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov–Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to $H_{\mathrm{\infty }}$ performance analysis and robust $H_{\mathrm{\infty }}$ controller design, using linear matrix inequalities (LMIs). Two numerical examples are presented that illustrate the effectiveness of the proposed method.

KEYWORDS:

• 2D continuous systems
• interval time-varying delays
• Wirtinger inequality
• delay-dependent
• robust $H_{\mathrm{\infty }}$ control
• LMIs

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Fernando Tadeo http://orcid.org/0000-0002-4046-3136

Additional information

Funding

Prof. Tadeo is funded by Consejería de Educación, Junta de Castilla y Leon, and FEDER funds (CLU 2017-09 and UIC 233).

Notes on contributors

Khalid Badie

Khalid Badie received his Master degree in Automatic Signals and Systems from University of Sidi Mohammed Ben Abdellah, Faculty of Sciences, Fez, Morocco in 2016. He is now studying for the PhD in Automatic Control in the National School of Applied Sciences, Fez. His current research interests include two-dimensional systems, fuzzy systems, switched systems, H8 control and filtering.

Mohammed Alfidi

Mohammed Alfidi received his PhD in Control and Automation from the Faculty of Sciences Dhar Elmehraz, Fes University Morocco in 2009. Since 2010, he has been a Professor and Head of the Industrial Department, at the National School of Applied Sciences, Fez University Morocco, from 2010. He has published more than 20 papers in various international journals and conferences. His research interests include automation, modelling, intelligent control, robust control, and multidimensional systems.

Fernando Tadeo

Fernando Tadeo is a currently a full Professor at the School of Engineering of the University of Valladolid, Spain, leading a multidisciplinary research group in Advanced Process Control. He graduated from the University of Valladolid, in Physics in 1992, and in Electronic Engineering in 1994. After completing an MSc in Control Engineering in the University of Bradford, UK with the top mark of the class, he went back to Valladolid, where he got his PhD degree in Automatic Control, with Honors. His main interest area is Control Systems with Constraints, in particular Positive Systems. This research is focused on applications in Process Control (In particular in Desalination) and in Renewable Energies (Wind, Solar and Osmotic Energies). As a result of this research he is coauthor of around 90 papers in international journals, more than 200 conference publications and co-author of two books.

Zakaria Chalh

Zakaria Chalh received his PhD in Control and Automation from Central Graduate School, France in 2008. Since 2011, he has been a professor at the National School of Applied Sciences, USMBA, Fez, Morocco. He has published more than 30 papers in various international journals and conferences. His research interests include automation, Bond Graph, modeling, intelligent control, Identification, robust control, and multidimensional systems.