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Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays

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Listed:
  • Yurong Liu
  • Yamin Wang
  • Xinquan Zhu
  • Xiaohui Liu

Abstract

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov–Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Yurong Liu & Yamin Wang & Xinquan Zhu & Xiaohui Liu, 2014. "Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1528-1538, July.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:7:p:1528-1538
    DOI: 10.1080/00207721.2013.849775
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    References listed on IDEAS

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    1. Zhicheng Li & Guanghui Sun & Huijun Gao, 2013. "Guaranteed cost control for discrete-time Markovian jump linear system with time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(7), pages 1312-1324.
    2. E. K. Boukas & Z. K. Liu, 2001. "Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 587-600, June.
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