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Admissibility analysis of linear singular systems via a delta operator method

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  • Xin-zhuang Dong

Abstract

In this paper, the problem of admissibility analysis is investigated for linear singular systems through a delta operator method. The delta operator model of a linear singular continuous system is set up first for a special case and then generalised to the common case. It is shown that when the sampling period tends to zero, the delta operator model tends to the corresponding singular continuous system. In order to obtain the above delta operator model, we adopt a linear singular discrete model which contains the sampling period instead of the standard discrete one which contains no sampling period in the modeling process. The relation between the admissibility of the two singular discrete models is analysed and it is proved that the admissibility of one singular discrete model is equivalent to that of the other discrete model. Moreover, based on the relation between the discrete and delta operator models, some admissibility conditions are derived for linear singular delta operator systems. A numerical example is also provided to demonstrate the theoretical results in this paper.

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  • Xin-zhuang Dong, 2014. "Admissibility analysis of linear singular systems via a delta operator method," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(11), pages 2366-2375, November.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:11:p:2366-2375
    DOI: 10.1080/00207721.2013.769646
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    References listed on IDEAS

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    1. Chih-Peng Huang, 2013. "Stability analysis and controller synthesis for fuzzy descriptor systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 23-33.
    2. Junchao Ren & Qingling Zhang, 2013. "Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(3), pages 450-460.
    3. Zheng-Guang Wu & Peng Shi & Hongye Su & Jian Chu, 2012. "Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(11), pages 2095-2106.
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