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Tracking Control Design for Markov Jump Systems With Time-varying Delay and External Disturbances

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  • Control Theory and Applications
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Abstract

This article intends to provide an effective output tracking control protocol and enhanced disturbance rejection performance for a class of continuous-time Markov jump systems (MJSs) with time-varying delay and external disturbances. Precisely, enhanced EID strategy combined with a proportional integral control is proposed to solve the output tracking problem for the addressed systems. In particular, an enhanced EID strategy can deal with the system flexibility and to increase disturbance rejection performance. The needed gain values for assuring the mean-square asymptotic stability of the MJSs are identified with the help of the Lyapunov-Krasovskii functional and linear matrix inequalities. The approach described in this paper can improve output tracking and disturbances rejection performance than some exiting results, which is explored through simulation results. Moreover, the legality of theoretical explorations is also verified by the RLC series circuit model.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Anna University, Regional Campus, Coimbatore, 641046, India

    Muthusamy Vijayakumar & Selvaraj Marshal Anthoni

  2. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641046, India

    Rathinasamy Saklhivel

  3. Department of Communications and Networks Engineering, Prince Sultan University, Riyadh, Saudi Arabia

    Dhafer Almakhles

Authors
  1. Muthusamy Vijayakumar
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  2. Rathinasamy Saklhivel
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  3. Dhafer Almakhles
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  4. Selvaraj Marshal Anthoni
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Correspondence to Muthusamy Vijayakumar.

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Compliance with Ethical Standards

The authors declare that there is no conflict of interest. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Muthusamy Vijayakumar completed his B.Sc. and M.Sc. degrees in the field of mathematics from Bharathiar University, Coimbatore, India, in 2014 and 2016, respectively. He is currently pursuing a Ph.D. degree with the Department of Mathematics, Anna University Regional Campus, Coimbatore, India. His current research interests include dynamical systems and control theory.

Rathinasamy Sakthivel received his B.Sc., M.Sc., M.Phil., and Ph.D. degrees in mathematics from Bharathiar University, Coimbatore, India, in 1992, 1994, 1996, and 1999, respectively. He served as a Lecturer with the Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore, from 2000 to 2001. From 2001 to 2003, he was a Post-Doctoral Fellow with the Department of Mathematics, Inha University, Incheon, Korea. From 2003 to 2005, he was a Japan Society for the Promotion of Science (JSPS) Fellow with the Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Kitakyushu, Japan. He was a Research Professor with the Department of Mathematics, Yonsei University, Seoul, Korea, till 2006. He was a Post-Doctoral Fellow (Brain Pool Program) with the Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, Korea, from 2006 to 2008. He served as an Assistant and Associate Professor with the Department of Mathematics, Sungkyunkwan University, Suwon, Korea from 2008 to 2013. From 2013 to 2016, he was a Professor at the Department of Mathematics, Sri Ramakrishna Institute of Technology, India. He is currently a Professor with the Department of Applied Mathematics, Bharathiar University, Coimbatore, India, since 2016. He has published over 380 research papers in reputed Science Citation Index journals. His current research interests include systems and control theory, optimization techniques, and nonlinear dynamics. He jointly with his foreign research collaborators, published a book and a good number of book chapters in Springer. He has visited Japan, Malaysia, Korea, Brazil, Germany, Australia, China and Saudi Arabia as a Visiting Researcher. He has continuously received the most coveted “Highly Cited Researcher” Award for the years 2017, 2018, 2019 and 2020, consecutively from the Clarivate Analytics, USA. He has been on the Editorial Board of international journals, including IEEE Access, Journal of the Franklin Institute, Neurocomputing, Neural Processing Letters, Mathematics and Journal of Electrical Engineering & Technology.

Dhafer Almakhles received his B.E. degree in electrical engineering from the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, in 2006, and his master’s (Hons.) and Ph.D. degrees from The University of Auckland, New Zealand, in 2011 and 2016, respectively. Since 2016, he has been with Prince Sultan University, Saudi Arabia, where he is currently the Head of the Communications and Networks Engineering Department. He is also the Director of the Science and Technology Unit and Intellectual Property Office, Prince Sultan University. He is also the Leader of the Renewable Energy Research Team and Laboratory. His research interests include power electronics, control theory, crewless aerial vehicles, renewable energy systems, and FPGA applications. He is a member of the IEEE Power Electronics and the IEEE Control Society. He is a Reviewer Member of various international journals and conferences, including the IEEE and IET.

Selvaraj Marshal Anthoni received his M.Sc. and Ph.D. degrees in mathematics from Bharathiar University, Coimbatore, India, in 1995 and 2001, respectively. He was a Lecturer with the Department of Mathematics, Kumaraguru College of Technology, Coimbatore, from 2001 to 2003. From 2003 to 2004, he was a Postdoctoral Fellow with the Department of Mathematics, Yonsei University, Korea. After that, he was a Lecturer with the Department of Mathematics, Periyar University, Salem, India, from 2004 to 2008. He is currently an Associate Professor in mathematics with the Anna University Regional Campus, Coimbatore. His research interests include control theory and abstract differential equations. He is an active Reviewer Member of various SCI/SCIE journals.

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Vijayakumar, M., Saklhivel, R., Almakhles, D. et al. Tracking Control Design for Markov Jump Systems With Time-varying Delay and External Disturbances. Int. J. Control Autom. Syst. 21, 2210–2222 (2023). https://doi.org/10.1007/s12555-021-0884-4

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