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On exponential and L2-exponential stability of continuous-time delay-difference systems

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  • Li, Zhao-Yan
  • Zhang, Qianqian
  • Zhou, Bin

Abstract

In this paper, the exponential stability (ES) and L2-exponential stability (L2-ES) of continuous-time delay-difference systems are studied. Firstly, the relationship between ES and L2-ES of the studied system is systematically presented. Secondly, a novel Lyapunov stability theorem is proposed to test both the ES and L2-ES with a guaranteed convergence rate of the system. Then, for a particular class of delay-difference systems with both point delays and distributed delays having exponential integral kernels, some stability criteria based on linear matrix inequalities (LMIs) are established by selecting suitable Lyapunov-Krasovskii functionals (LKFs) and using a delay decomposition technique. Finally, a numerical example is worked out to illustrate the effectiveness of the theoretical results.

Suggested Citation

  • Li, Zhao-Yan & Zhang, Qianqian & Zhou, Bin, 2024. "On exponential and L2-exponential stability of continuous-time delay-difference systems," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324004107
    DOI: 10.1016/j.amc.2024.128949
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    References listed on IDEAS

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    1. Feng, Zhiguang & Zhang, Xinyue & Lam, James & Fan, Chenchen, 2023. "Estimation of reachable set for switched singular systems with time-varying delay and state jump," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    2. Zhai, Zhengliang & Yan, Huaicheng & Chen, Shiming & Chang, Yufang & Zhou, Jing, 2024. "Novel stability criteria of generalized neural networks with time-varying delay based on the same augmented LKF and bounding technique," Applied Mathematics and Computation, Elsevier, vol. 460(C).
    3. Wang, Yibo & Hua, Changchun & Park, PooGyeon & Qian, Cheng, 2023. "Stability criteria for time-varying delay systems via an improved reciprocally convex inequality lemma," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Zeng, Xu & Li, Chuandong & Huang, Tingwen & He, Xing, 2015. "Stability analysis of complex-valued impulsive systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 75-82.
    5. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
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