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Delay-dependent H ∞ control for a class of uncertain time-delay singular Markovian jump systems via hybrid impulsive control

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  • Control Theory and Applications
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Abstract

This paper deals with the problem of robust normalization and delay-dependent H ∞ control for a class of singular Markovian jump systems with norm-bounded parameter uncertainties and time delay. A new impulsive and proportional-derivative control strategy with memory is presented, which results in a novel class of hybrid impulsive systems. Sufficient conditions are developed to guarantee that the resultant closed-loop system is not only robust normal and stochastically stable, but also satisfies a prescribed H ∞ performance level for all delays no larger than a given upper bound. In addition, the explicit expression of the desired impulsive control gains is also given together with the design approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

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Authors and Affiliations

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

    Hui Lv & Junchao Ren

  2. Institute of Systems Science, Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang, 110819, China

    Qingling Zhang

Authors
  1. Hui Lv
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  2. Qingling Zhang
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  3. Junchao Ren
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Corresponding author

Correspondence to Qingling Zhang.

Additional information

Recommended by Associate Editor Yingmin Jia under the direction of Editor PooGyeon Park. This work was supported by the National Natural Science Foundation of China under Grants 61273008 and 61203001.

Hui Lv received her B.S. and M.S. degrees in applied mathematics from Liaoning University, Shenyang, China, in 2004 and 2009, respectively. She is pursuing a Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China. Her research interests include singular Markovian systems and impulsive control.

Qingling Zhang received the B.S. and M.S. degrees from the Mathematics Department and the Ph.D. degree from the Automatic Control Department of Northeastern University, Shenyang, China, in 1982, 1986 and 1995, respectively. Dr. Zhang is now a Professor at Institute of Systems Science, Northeastern University. His research interests include singular systems and stochastic systems.

Junchao Ren received his B.S. degree in applied mathematics from Northeastern University, Shenyang, China, in 2000 and an M.S. degree in control theory and control engineering from Guangdong University of Technology, Guangzhou, in 2003 and a Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2011. Dr. Ren is currently an associate professor with Institute of Systems Science, Northeastern University, Shenyang, China. His research interests include robust control and singular systems.

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Lv, H., Zhang, Q. & Ren, J. Delay-dependent H ∞ control for a class of uncertain time-delay singular Markovian jump systems via hybrid impulsive control. Int. J. Control Autom. Syst. 14, 939–947 (2016). https://doi.org/10.1007/s12555-015-0097-9

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  • DOI: https://doi.org/10.1007/s12555-015-0097-9

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