Sliding Mode Control for a Class of Nonlinear Positive Markov Jumping Systems with Uncertainties in a Finite-time Interval

Abstract

This paper studies the finite-time sliding mode control problem for a class of nonlinear positive Markov jumping systems with uncertain parameters. Firstly, a mode-dependent sliding mode surface is designed to guarantee the positiveness and finite-time boundedness of the closed-loop Markov jumping systems. Then, a suitable finite-time sliding mode controller is given to guarantee the closed-loop MJSs can drive onto the specified sliding mode surface during a given finite-time interval and then maintain on the sliding surface. Based on the stochastic Lyapunov-Krasovskii functional approach and linear matrix inequalities technique, sufficient conditions on the existence of the finite-time controller are proposed and proved. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

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Corresponding author

Correspondence to Shuping He.

Additional information

Recommended by Editor Hamid Reza Karimi. This work was supported in part by the National Natural Science Foundation of P. R. China under Grant 61673001, 61203051, the Foundation for Distinguished Young Scholars of Anhui Province under Grant 1608085J05, the Key Support Program for University Outstanding Youth Talent of Anhui Province under Grant gxydZD2017001 and the open fund for Discipline Construction, Institute of Physical Science and Information Technology, Anhui University.

Chengcheng Ren received the B.S. degree in measurement and control technology and instrument from Anhui University of Technology, Maanshan, China, in 2011. He received the Master degree in control theory and control engineering in Anhui University, Hefei, China in 2018. Now, he is currently pursuing a Ph.D. degree with the School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China. His current research interests include positive systems, nonlinear control and optimal control.

Shuping He received the B.S. degree in automation and Ph.D degree in control theory and control engineering in Jiangnan University, Wuxi, China, in 2005 and 2011, respectively. From 2010 to 2011, he was a visiting scholar with the Control Systems Centre, The University of Manchester, UK. From 2011 to 2013, he was successively a senior lecturer in Anhui University. Since 2013, he has been a professor with School of Electrical Engineering and Automation, Anhui University, Hefei, China. His current research focuses on control theory and control systems, signal processing and artificial intelligence.

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Ren, C., He, S. Sliding Mode Control for a Class of Nonlinear Positive Markov Jumping Systems with Uncertainties in a Finite-time Interval. Int. J. Control Autom. Syst. 17, 1634–1641 (2019). https://doi.org/10.1007/s12555-018-0793-3

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Keywords

  • Finite-time boundedness
  • positive Markov jumping systems
  • sliding mode control