Robust H_∞ filtering for 2D continuous systems with finite frequency specifications

ABSTRACT

This paper investigates the design problem of robust H_∞ filtering for uncertain two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties and frequency domain specifications. Our aim is to design a new filter guaranteeing an H_∞ performance level in specific finite frequency (FF) domains. Using the well-known generalised Kalman Yakubovich Popov lemma and homogeneous polynomially parameter-dependent matrices of arbitrary degrees, sufficient conditions for the existence of H_∞ filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities. Illustrative examples are provided to show the usefulness and potential of the proposed results.

KEYWORDS:

• Multi-dimensional systems
• Lyapunov approach
• Roesser models
• finite frequency domain
• H_∞ filtering

Acknowledgment

The authors would like to thank the anonymous reviewers and editors for their useful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Abderrahim El-Amrani

Abderrahim El-Amrani was born in Taounate, morocco, in 1990. Recieved his Master degree in signals, systems and informatics from the Faculty of Sciences at University Of Sidi Mohamed Ben Abdelah, Morocco, in 2014. He is currently pursuing the Ph.D. degree at Sidi Mohammed ben Abdellah University. The main research interests Include finite frequency, two-dimensional (2-D) systems, robust control and Fuzzy Systems.

Bensalem Boukili

Bensalem Boukili was born in Taounate, morocco, in 1977. He received the Ph.D degree in electrical engineering from the Faculty of Sciences, Dhar El Mahraz, Fez, Morocco, in 2014. His research interests are delay systems, stability theory, systems with constraints and 2-D systems.

Abdellaziz Hmamed

Abdelaziz Hmamed was born in sefrou, morocco, in 1951. He received the doctorate of state degree in electrical engineering from the Faculty of Sciences, Rabat, Morocco, in 1985. Since 1986 he has been with the department of Physics, Faculty of Sciences Dhar El Mehraz at Fez, where he is currently a full Professor. His research interests are delay systems, stability theory, systems with constraints and 2-D systems.

Ahmed El Hajjaji

Ahmed El Hajjaji received his Ph.D in automatic control from theUniversityOf Picardie Jules vernes, France in 1993. He was an associate Professor in the Same University from1994 to 2003.He is currently a full Professor in the same University. Since 2001, he has also been the head of the research team of control and vehicle of modeling, information and systems (MIS) laboratory. His current research interests include fuzzy control, vehicle dynamics, faulttolerant control, neural networks, manglev systems and renewable energy systems.

Ismail Boumhidi

Ismail Boumhidi is a professor of electronics at the Faculty of Sciences, Fez, Morocco. He received his Ph.D. degree from Sidi Mohammed ben Abdellah University, Faculty of Sciences, in 1999. His research areas include adaptive robust control, multivariable non-linear systems and fuzzy logic control with applications.