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Sliding mode control for descriptor Markovian jump systems with mode-dependent derivative-term coefficient

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Abstract

This paper concerns sliding mode control problems for a class of descriptor Markovian jump systems with mode-dependent derivative-term coefficient. Firstly, a necessary and sufficient condition, under which such type descriptor Markovian jump systems with mode-dependent derivative-term coefficient are stochastically admissible, is proposed by means of the strictly linear matrix inequality (LMI) technique. Then a novel sliding surface function, in terms of both system states and inputs, is proposed for descriptor Markovian jump systems with mode-dependent derivative-term coefficient and a dynamic sliding mode controller is synthesized, which ensures the reachability of predefined sliding surface in finite time. It is also shown that the stochastic admissibility of the overall closed loop systems can be determined by checking the feasibility of a series of LMIs. Finally, an illustrative example on DC motor is provided to demonstrate the effectiveness of the theoretical results.

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Acknowledgments

This work was supported by the Natural Science Foundation of China under Grant 61273008, the Natural Science Foundation of Liaoning Province under Grant 2014020019, the Nature Science of Foundation of Shenyang under Grant F14-231-1-02 and Science and Technology Research Fund of Liaoning Education Department under Grant L2013051, respectively.

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Authors and Affiliations

  1. Institute of Systems Science, Northeastern University, Shenyang, 110819, China

    Jinghao Li, Qingling Zhang & Ding Zhai

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China

    Qingling Zhang

  3. College of Science, Shenyang University of Technology, Shenyang, 110870, China

    Yi Zhang

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  1. Jinghao Li
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  2. Qingling Zhang
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  3. Ding Zhai
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  4. Yi Zhang
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Correspondence to Qingling Zhang.

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Li, J., Zhang, Q., Zhai, D. et al. Sliding mode control for descriptor Markovian jump systems with mode-dependent derivative-term coefficient. Nonlinear Dyn 82, 465–480 (2015). https://doi.org/10.1007/s11071-015-2168-0

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  • DOI: https://doi.org/10.1007/s11071-015-2168-0

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