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Adaptive Robust H∞ Sliding Mode Control for Singular Systems with Time-varying Delay and Uncertain Derivative Matrix

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Abstract

This paper considers the problem of sliding mode control (SMC) design for a class of nonlinear singular systems with time-varying delay and uncertainties, especially with uncertainties in the derivative matrix. By taking uncertainties of the derivative matrix into account, the state augmentation transformation is constructed such that uncertainties of the derivative matrix are eliminated. Then an appropriate integral-type sliding surface function is designed. And the resulting sliding mode dynamics is an uncertain singular time-varying delay system. A delay-dependent sufficient condition which guarantees the sliding mode dynamics to be admissible with H∞ performance is established. A new version of stabilization solvability condition is then proposed in terms of linear matrix inequality (LMI), which determines the undetermined parameter K in both the sliding surface function and the SMC laws. Moreover, two distinctive controllers (i.e., a SMC law and an adaptive SMC law) are synthesized such that the finite-time reachability of the predesigned sliding surface can be ensured. Finally, simulation examples are given to demonstrate the effectiveness and the merits of the proposed theory.

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Author information

Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China

    Qi Liu & Jianxun Li

  2. Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China

    Rongchang Li

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

    Qingling Zhang

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  1. Qi Liu
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  2. Rongchang Li
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  3. Qingling Zhang
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  4. Jianxun Li
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Corresponding author

Correspondence to Jianxun Li.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Guangdeng Zong under the direction of Editor Hamid Reza Karimi. This work was supported by the National Natural Science Foundation of China (No.61673265).

Qi Liu received his B.S. degree from Northeastern University, Shenyang, China, in 2018. He is currently pursuing a Ph.D. degree at Shanghai Jiao Tong University, Shanghai, China. His current research interests include singular systems, time-delay systems, sliding mode control, adaptive control, and robust control.

Rongchang Li received his B.E. degree from Qingdao University of Science and Technology, China, in 2016, and his M.S. degree from Northeastern University, Shenyang, China, in 2019. He is currently pursuing a Ph.D. degree at Peking University, Beijing, China. His current research interests include singular systems, fuzzy control, and sliding mode observer design.

Qingling Zhang received his B.S., M.S., and Ph.D. degrees from Northeastern University, Shenyang, China, in 1982, 1986, and 1995, respectively. He finished his two-year postdoctoral work in Automatic Control Department of Northwestern Polytechnical University, Xi’an, China, in 1997. His research interests include biomodeling and biocybernetics, differential and algebraic systems, and matrix theory and application.

Jianxun Li received his Ph.D. degree from Northwestern Polytechnical University, Xi’an, China, in 1996. From 1997 to 1999, he joined Xidian University, Xi’an, China, as a postdoctoral fellow. He was a visiting professor at Imperial College London from 2006 to 2007. He is currently a professor at School of Electronic Information and Electric Engineering, Shanghai Jiao Tong University, Shanghai, China. His research interests include control theory and application, information fusion, infrared image processing, and parameter estimation.

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Liu, Q., Li, R., Zhang, Q. et al. Adaptive Robust H∞ Sliding Mode Control for Singular Systems with Time-varying Delay and Uncertain Derivative Matrix. Int. J. Control Autom. Syst. 17, 3179–3193 (2019). https://doi.org/10.1007/s12555-019-0048-y

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