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Positivity and stability of timescale-type linear singular systems with time delays

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Abstract

This paper investigates positivity and stability problems of timescale-type delayed linear singular systems (LSSs). The existing results put an extremely strict constraint on the time-delay function. By introducing a novel function, this constraint is successfully removed, which generalizes the scope of the considered systems. Then, some necessary and sufficient criteria are proposed for the positivity of LSSs with bounded and infinite time-varying delays. Finally, the exponential (asymptotical) stability of LSSs with bounded (infinite) time-varying delays is analyzed. The derived results are also applicable to timescale-type differential-difference systems (DDSs). Compared with the existing stability criteria of DDSs with bounded time-varying delays, the strict limit on the parameter related to the convergence rate is eliminated. Hence, the conservatism of the existing results can be reduced. Moreover, when investigating stability of DDSs with infinite time-varying delays, this paper proposes a less conservative stability theorem. To illustrate the validity of the derived results, an example is presented regarding LSSs with bounded and infinite time-varying delays.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 62003195, 62073202).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250358, China

    Xiaodong Lu & Haitao Li

  2. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaodong Lu

  3. School of Control Science and Engineering, Shandong University, Jinan, 250014, China

    Xianfu Zhang

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  1. Xiaodong Lu
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  2. Haitao Li
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  3. Xianfu Zhang
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Correspondence to Xiaodong Lu.

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Lu, X., Li, H. & Zhang, X. Positivity and stability of timescale-type linear singular systems with time delays. Sci. China Inf. Sci. 65, 222201 (2022). https://doi.org/10.1007/s11432-022-3517-7

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  • DOI: https://doi.org/10.1007/s11432-022-3517-7

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