Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities

This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.Keywords: 2D stochastic systemsrandomly occurring uncertaintiesrandomly occurring nonlinearitieslinear matrix inequality (LMI) AcknowledgementsThe third author would like to thank the Alexander-von-Humboldt Foundation for providing the support to this research possible. The authors are also grateful to the anonymous reviewers for their helpful comments.Additional informationFundingThis work was supported by the National Natural Science Foundation of China under [grant number 61273120].Notes on contributorsZhaoxia DuanZhaoxia Duan was born in Sichuan Province, China, in 1989. She received her BS degree in Automation from Nanjing University of Science and Technology (NUST), Nanjing, China, in 2011. Now she is pursuing a PhD degree in Control Theory and Control Engineering from NUST, Nanjing, China. Her current research interests include robust control and filtering, switched systems, two-dimensional systems and nonlinear systems. Display full sizeZhengrong XiangZhengrong Xiang received his PhD degree in Control Theory and Control Engineering at Nanjing University of Science and Technology, Nanjing, China, in 1998. Since 1998, he has been faculty member and he is currently full professor at Nanjing University of Science and Technology. He was appointed as Lecturer in 1998 and Associate Professor in 2001 at Nanjing University of Science and Technology. He is a member of the IEEE, member of the Chinese Association for Artificial Intelligence. His main research interests include switched systems, nonlinear control, robust control and networked control systems. Display full sizeHamid Reza KarimiHamid Reza Karimi is a Professor in Control Systems at the Faculty of Engineering and Science of the University of Agder in Norway. His research interests are in the areas of nonlinear systems, networked control systems, robust control/filter design, time-delay systems, wavelets and vibration control of flexible structures with an emphasis on applications in engineering. He is a senior member of IEEE and serves as chairman of the IEEE chapter on control systems at IEEE Norway section. He is also serving as an editorial board member for some international journals, such as Mechatronics, Neurocomputing, Information Sciences, Asian Journal of Control, Journal of Franklin Institute, Journal of Systems and Control Engineering, and International Journal of Control, Automation and Systems. He is a member of IEEE Technical Committee on Systems with Uncertainty, IFAC Technical Committee on Robust Control and IFAC Technical Committee on Automotive Control. Display full size