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Global exponential stability of impulsive switched positive nonlinear systems with mode-dependent impulses

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  • Kang, Yu
  • Zhang, Niankun
  • Chen, Guoyong

Abstract

The global exponential stability for a type of continuous-time impulsive switched positive nonlinear systems (ISPNSs) with average dwell time (ADT) switching and mode-dependent impulsive effects is explored in this research. Where we consider a type of nonnegative impulses, which do not need to be in step with the switching behaviors in the constructed systems. The main challenge of this study comes from the estimation of Lyapunov functions within any time interval under the coupling effect of asynchronous switches and state jumps. To solve this difficulty, based on the multiple max-separable Lyapunov functions (MSLFs) method involving mode-dependent average impulsive interval (MDAII) approach, we consider two special cases in which switching and impulses are completely asynchronous and synchronous respectively, and successfully establish the relation of impulse strength, system modes, ADT and MDAII. Subsequently, several stability criteria are presented for ISPNSs with unstable and/or stable modes. In particular, the impact of various sorts of impulses on stability are also analysed in depth. Then, the obtained results are applied to the ISPNSs with synchronous impulses and switching. Moreover, the stability conditions of the considered systems without switches are gained directly, which enshrouds the existing results.

Suggested Citation

  • Kang, Yu & Zhang, Niankun & Chen, Guoyong, 2023. "Global exponential stability of impulsive switched positive nonlinear systems with mode-dependent impulses," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005896
    DOI: 10.1016/j.amc.2022.127515
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    References listed on IDEAS

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    1. Ding, Xiuyong & Liu, Xiu, 2017. "On stabilizability of switched positive linear systems under state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 92-101.
    2. Li, Shuo & Xiang, Zhengrong, 2020. "Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    3. Wang, Huajian & Qi, Wenhai & Zhang, Lihua & Cheng, Jun & Kao, Yonggui, 2020. "Stability and stabilization for positive systems with semi-Markov switching," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    4. Liang, Mengqian & Tian, Yazhou, 2022. "Practical stability of switched homogeneous positive nonlinear systems: Max-separable Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    5. Sun, Yuangong & Tian, Yazhou, 2022. "Polynomial stability of positive switching homogeneous systems with different degrees," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    6. Xi, Qiang & Liu, Xinzhi, 2020. "Mode-dependent impulsive control of positive switched systems: Stability and L1-gain analysis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Ju, Yanhao & Sun, Yuangong & Meng, Fanwei, 2020. "Stabilization of switched positive system with impulse and marginally stable subsystems: A mode-dependent dwell time method," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    8. Zhang, Jie & Sun, Yuangong, 2021. "Practical exponential stability of discrete-time switched linear positive systems with impulse and all modes unstable," Applied Mathematics and Computation, Elsevier, vol. 409(C).
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    Cited by:

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    3. Zhong, Yuguang & Song, Dening, 2023. "Nonfragile synchronization control of T-S fuzzy Markovian jump complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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