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New insight into reachable set estimation for uncertain singular time-delay systems

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  • Liu, Guobao
  • Xu, Shengyuan
  • Wei, Yunliang
  • Qi, Zhidong
  • Zhang, Zhengqiang

Abstract

This paper investigates the problem of reachable set estimation for a class of uncertain singular systems with time-varying delays from a new point of view. Our consideration is centered on the design of a proportional-derivative state feedback controller (PDSFC) such that the considered singular system is robustly normalizable and all the states of the closed-loop system can be contained by a bounded set under zero initial conditions. First, a nominal singular time-delay system is considered and sufficient conditions are obtained in terms of matrix inequalities for the existence of a PDSFC and an ellipsoid. In this case, the considered system is guaranteed to be normalizable and the reachable set of the closed-loop systems is contained by the ellipsoid. Then, the result is extended to the case of singular time-delay systems with polytopic uncertainties and relaxed conditions are derived by introducing some weighting matrix variables. Furthermore, based on the obtained results, the reachable set of the considered closed-loop singular system can be contained in a prescribed ellipsoid. Finally, the effectiveness of our results are demonstrated by two numerical examples.

Suggested Citation

  • Liu, Guobao & Xu, Shengyuan & Wei, Yunliang & Qi, Zhidong & Zhang, Zhengqiang, 2018. "New insight into reachable set estimation for uncertain singular time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 769-780.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:769-780
    DOI: 10.1016/j.amc.2017.10.035
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    References listed on IDEAS

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    1. Fu, Lei & Ma, Yuechao, 2016. "Passive control for singular time-delay system with actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 181-193.
    2. Yueqiao Han & Yonggui Kao & Cunchen Gao & Baoping Jiang, 2017. "Robust sliding mode control for uncertain discrete singular systems with time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 818-827, March.
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    5. Chen, Jian & Lin, Chong & Chen, Bing & Wang, Qing-Guo, 2017. "Mixed H∞ and passive control for singular systems with time delay via static output feedback," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 244-253.
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    Cited by:

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    7. Liu, Shouqiang & Yu, Mengjing & Li, Miao & Xu, Qingzhen, 2019. "The research of virtual face based on Deep Convolutional Generative Adversarial Networks using TensorFlow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 667-680.
    8. Shafiya, M. & Nagamani, G. & Dafik, D., 2022. "Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 168-186.
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