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Volume 8 Issue 1
Jan.  2021

IEEE/CAA Journal of Automatica Sinica

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Xian-Ming Zhang, Qing-Long Han and Xiaohua Ge, "Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 77-85, Jan. 2021. doi: 10.1109/JAS.2020.1003111
Citation: Xian-Ming Zhang, Qing-Long Han and Xiaohua Ge, "Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 77-85, Jan. 2021. doi: 10.1109/JAS.2020.1003111

Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

doi: 10.1109/JAS.2020.1003111
Funds:  This work was supported in part by the Australian Research Council Discovery Project (Grant No. DP160103567)
More Information
  • One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay. The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval. The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer. The second contribution of this paper is to introduce a novel Lyapunov-Krasovskii functional, which includes a cubic polynomial on a time-varying delay, in stability analysis of time-delay systems. Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities, two stability criteria are derived for two cases of the time-varying delay. A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

     

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    Highlights

    • Establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval;
    • Introduce a novel Lyapunov-Krasovskii functional;
    • The proposed stability criteria are of less conservativeness than some existing ones

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