On ℓ₂–ℓ∞ output-feedback control scheduled by stochastic communication protocol for two-dimensional switched systems

Abstract

This paper is concerned with the ${\ell }_2$–${\ell }_{\mathrm{\infty }}$ output-feedback control problem for a class of two-dimensional (2-D) switched systems described by the general Fornasini–Marchesini second model under the stochastic communication protocol (SCP). In a networked 2-D switched control system, the sensors and the controller are typically connected through a shared communication network of limited bandwidth, which is likely to result in data collision problem. To circumvent this network-induced problem, a new SCP is dedicatedly put forward for the 2-D switched system in order to orchestrate the transmission order of sensor nodes, under which only one sensor node obtains the privilege to access the network at each transmission instant. Then, based on the nominal system information compensation, a set of new mode-dependent output-feedback controllers is designed for 2-D switched systems subject to SCP and external disturbances. Moreover, using the average dwell-time approach, sufficient conditions are established to ensure the existence of the desired controllers that guarantee both the exponential mean-square stability and the ${\ell }_2$–${\ell }_{\mathrm{\infty }}$ performance. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed controller design method.

Keywords:

• Two-dimensional switched systems
• Fornasini–Marchesini second model
• average dwell-time
• ${\ell }_2$–${\ell }_{\mathrm{\infty }}$ control
• stochastic communication protocol

Disclosure statement

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

Additional information

Funding

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah [grant number RG-21-135-41]. The authors, therefore, acknowledge with thanks DSR for technical and financial support. This work was also supported in part by the National Natural Science Foundation of China [grant numbers 61773017 and 61773144], the Outstanding Youth Science Foundation of Heilongjiang Province of China [grant number JC2018001], the Fundamental Research Foundation for Universities of Heilongjiang Province of China [grant number 2019-KYYWF-0215], and the Alexander von Humboldt Foundation of Germany.

Notes on contributors

Kaiqun Zhu

Kaiqun Zhu received the M.Sc. degree in control science and engineering, in 2018, from University of Shanghai for Science and Technology, Shanghai, China, where he is currently pursuing his Ph.D. degree. Since 2020, he has been a visiting Ph.D. student with the Department of Computer Science, Brunel University London, Uxbridge, U.K. His current research interests include set-membership filtering, model predictive control, and neural networks.

Jun Hu

Jun Hu received the B.Sc. degree in Information and Computation Science and M.Sc. degree in Applied Mathematics from Harbin University of Science and Technology, Harbin, China, in 2006 and 2009, respectively, and the Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2013. From September 2010 to September 2012, he was a Visiting Ph.D. Student in the Department of Information Systems and Computing, Brunel University, U.K. From May 2014 to April 2016, he was an Alexander von Humboldt research fellow at the University of Kaiserslautern, Kaiserslautern, Germany. He is a Professor and Ph.D. supervisor in the Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China. His research interests include nonlinear control, filtering and fault estimation, time-varying systems and complex networks. He has published more than 70 papers in refereed international journals. Prof. Hu serves as a reviewer for Mathematical Reviews, as an editor for Neurocomputing, Journal of Intelligent and Fuzzy Systems, Neural Processing Letters, Systems Science and Control Engineering, and as a guest editor for International Journal of General Systems and Information Fusion.

Yurong Liu

Yurong Liu received the B.Sc. degree in mathematics from Suzhou University, Suzhou, China, in 1986, the M.Sc. degree in applied mathematics from the Nanjing University of Science and Technology, Nanjing, China, in 1989, and the Ph.D. degree in applied mathematics from Suzhou University in 2000. He is currently a Professor with the Department of Mathematics, Yangzhou University, Yangzhou, China. He has published over 100 papers in international journal. His current interests include neural networks, nonlinear dynamics, time-delay systems, and chaotic dynamics. He serves as an editorial board member for Neurocomputing.

Naif D. Alotaibi

Naif D. Alotaibi completed the B.Sc. in Computer Engineering from the King Abdulaziz University in Jeddah, Saudi Arabia, in 2000, and received his M.Sc. and Ph.D. degrees in Information Technology from Queensland University of Technology in Brisbane, Australia, in 2006 and 2012, respectively. In 2013, he joined the Electrical and Computer Engineering Department at the Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia as an assistant professor. His research interests include IT infrastructure, computer network quality and network QoS, and quality measurement.

Fuad E. Alsaadi

Fuad E. Alsaadi received the B.S. and M.Sc. degrees in electronic and communication from King Abdulaziz University, Jeddah, Saudi Arabia, in 1996 and 2002, respectively, and the Ph.D. degree in optical wireless communication systems from the University of Leeds, Leeds, U.K., in 2011. From 1996 to 2005, he was a Communication Instructor with the College of Electronics and Communication, Jeddah. He is currently an Associate Professor with the Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University. He has published widely in the top IEEE communications conferences and journals. His current research interests include optical systems and networks, signal processing, and synchronization and systems design. He was a recipient of the Carter Award, University of Leeds for the best Ph.D.