Non-fragile mixed H_∞/passive-based asynchronous sliding mode control for nonlinear singular Markovian jump systems

Abstract

In this paper, the problem of asynchronous sliding mode control (SMC) is addressed for discrete-time singular Markovian jump systems (DSMJSs) with external disturbances and randomly occurring nonlinearities. Moreover, the states of DSMJSs are unavailable for measurement, and the synchronisation between the controller and the system modes is not surely ensured. Our attention is mainly focused on solving the control problem by proposing an observer-based adaptive sliding mode controller for such a class of complex systems. First, a non-fragile observer is designed not only to estimate the system states but also to relax the multiplicative gain variations and to construct an appropriate mode-dependent sliding mode surface function. Then, by assuming that the bounds of nonlinear terms are unknown, an adaptive SMC control law is synthesised to drive the system trajectories onto the specified sliding surface and completely compensate for the influences of the external disturbances and fluctuations of the controller and observer gains. Sufficient conditions are established to ensure that the closed-loop system is stochastically admissible with a γ level of the mixed $H_{\mathrm{\infty }}$/passive performance, and to provide the observer and controller gain matrices. Finally, to numerically substantiate the efficacy of the proposed control scheme, two examples are given.

Keywords:

• Singular Markovian jump system
• asynchronous jumps
• non-fragile control
• SMC
• mixed $H_{\mathrm{\infty }}$/passivity

Disclosure statement

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

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This research has been funded by Scientific Research Deanship at University of Hail-Saudi Arabia through project number RG20114.

Notes on contributors

Mourad Kchaou

Mourad Kchaou received his PhD. degree in Automatic Control from the National School of Engineering, university of Sfax, Tunisia, in 2009. Currently, he is a professor with the Department of Electrical Engineering, University of Hail, Saudi Arabia. Since 2000, he holds a researcher position at the Laboratory of Sciences and Techniques of Automation Control and Computer Engineering, National Engineering School of Sfax, University of Sfax, Tunisia. He has published more than 100 scientific papers and book chapters. His research interests include fuzzy control, time-delay systems, singular systems and robust control.

Houssem Jerbi

Houssem Jerbi was born in Tunisia on October 20, 1971. He received the Ph.D. degree in Electrical Engineering from the ENIT – University of Al Manar, Tunis, TUNISIA, in 2000. He is currently an Associate Professor in the Department of Industrial Engineering, College of Engineering, at the University of Hail - KSA and has been the main consultant of the GDPMO – UOH since 2014. From 2000 to 2010, he was an Assistant Professor in the College of Science of Sfax Tunisia. Since 2010, he has been a faculty member at the University of HAIL - KSA. He has published more than 100 scientific papers and book chapters in the field of nonlinear control and systems robotics and power electronics. His research interests include stability analysis, advanced control, big data control system engineering and fault tolerant control. He is currently belonging to different research groups in Hail University with the major subject of based artificial intelligence applications.

Belgacem Toual

Belgacem Toual was born in Djelfa, Algeria in 1969. He is actually an associate Professor at the University of Djelfa, Algeria. He is a member of the Scientific Council of the Faculty of Sciences and Technology and president of the Scientific Committee of the Electrical Engineering Department. He published several papers. His main research interests include Hybrid Power Systems based on Renewable Power Sources, Power Quality issues, Power Electronics Devices, Application of Power Electronics in Renewable Energies, Application of Meta-heuristics Optimization Algorithms, Smart and Micro Grids and Reliability and Diagnostics in Power Electronics Converters and in other industrial applications.

Abdallah Kouzou

Professor Abdallah Kouzou (IEEE Senior member & IACSIT Senior member, IFAC, IAENG & IISRO member, IEEE-HKN Alumni Member) was born in Djelfa, Algeria in 1964. He is actually a Full Professor at the University of Djelfa, Algeria. He was the president of the Scientific Council of the faculty of Sciences and Technology from 2014 to 2015 and the Dean of the same faculty from 2015 to 2017. He has participated in several research projects and has led several research projects. He has published more than 360 papers, his main research interests include Active Power Filtering techniques, Power Quality issues, Power Electronics Devices, Application of Power electronics in Renewable Energies, Materials for multi-layers coating in PV cells. Multi-phase machines, Sensorless control, Application of meta-heuristics optimization algorithms, Smart Grid and Smart Buildings, reliability and diagnostics in power electronics converters and in other industrial applications, Non Destructive Testing and Measurement Techniques, Diagnosis and control of Gas Turbine of high power.