Skip to main content
SpringerLink
Log in

Finite-time stability of nonlinear time-varying systems with saturated impulse inputs

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The aim of this paper is to analyze the finite-time stability (FTS) of nonlinear time-varying systems with saturated impulse inputs and further analyze the finite-time contractive stability (FTCS). By employing theories of convex analysis, impulsive control, matrix inequality and Lyapunov function, several results about FTS and FTCS of nonlinear time-varying systems with saturated impulse inputs are obtained. The simulation examples show the validation of the proposed results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data availability

The data used to support the results of this study have been included in the simulation section of the article. In addition, the simulation code can be obtained from the corresponding author in a reasonable request.

References

  1. Amato, F., Ariola, M., Dorato, P.: Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9), 1459–1463 (2001)

    Article  MATH  Google Scholar 

  2. Barreau, M., Tarbouriech, S., Gouaisbaut, F.: Lyapunov stability analysis of a mass-spring system subject to friction. Syst. Control Lett. 150, 104910 (2021)

    Article  MATH  Google Scholar 

  3. Bitsoris, G.: Stability analysis of non-linear dynamical systems. Int. J. Control 38(3), 699–711 (1983)

    Article  MATH  Google Scholar 

  4. Cai, Z.W., Huang, L.H.: Finite-time synchronization by switching state-feedback control for discontinuous Cohen–Grossberg neural networks with mixed delays. Int. J. Mach. Learn. Cybern. 9(10), 1683–1695 (2018)

    Article  Google Scholar 

  5. Chen, G., Deng, F., Yang, Y.: Practical finite-time stability of switched nonlinear time-varying systems based on initial state-dependent dwell time methods. Nonlinear Anal. Hybrid Syst. 41, 101031 (2021)

    Article  MATH  Google Scholar 

  6. Chen, Z., Xie, Y.: Finite-time stability analysis of a class of nonlinear time-varying systems: a numerical algorithm. Int. J. Syst. Sci. 49(10), 2224–2242 (2018)

    Article  MATH  Google Scholar 

  7. Cheng, X., Guan, Z., Wang, Y.: Impulsive control for a class of uncertain systems with nonlinear perturbations. Syst. Eng. Electron. 4, 454–457 (2003). (in Chinese)

    Google Scholar 

  8. Dalir, M., Bigdeli, N.: An adaptive neuro-fuzzy backstepping sliding mode controller for finite time stabilization of fractional-order uncertain chaotic systems with time-varying delays. Int. J. Mach. Learn. Cybern. 12(7), 1949–1971 (2021)

    Article  Google Scholar 

  9. Feng, L., Zhao, P.: Finite-time stability and stabilization of switched linear time-varying systems with time-varying delay. Math. Probl. Eng. 2021, 1–8 (2021)

    Google Scholar 

  10. He, Z., Li, C., Cao, Z., Li, H.: Stability of nonlinear variable-time impulsive differential systems with delayed impulses. Nonlinear Anal. Hybrid Syst. 39, 100970 (2021)

    Article  MATH  Google Scholar 

  11. Hu, M.J., Wang, Y.W., Xiao, J.W.: On finite-time stability and stabilization of positive systems with impulses. Nonlinear Anal. Hybrid Syst. 31, 275–291 (2019)

    Article  MATH  Google Scholar 

  12. Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Springer Science, Berlin (2001)

    Book  MATH  Google Scholar 

  13. Hua, C., Jiang, A., Li, K.: Adaptive neural network finite-time tracking quantized control for uncertain nonlinear systems with full-state constraints and applications to quavs. Neurocomputing 440, 264–274 (2021)

    Article  Google Scholar 

  14. Jiang, B., Hu, Q., Friswell, M.I.: Fixed-time attitude control for rigid spacecraft with actuator saturation and faults. IEEE Trans. Control Syst. Technol. 24(5), 1892–1898 (2016)

    Article  Google Scholar 

  15. Joby, M., Santra, S., Anthoni, S.M.: Finite-time contractive boundedness of extracorporeal blood circulation process. Appl. Math. Comput. 388, 125527 (2021)

    MATH  Google Scholar 

  16. Kawano, Y.: Converse stability theorems for positive linear time-varying systems. Automatica 122, 109193 (2020)

    Article  MATH  Google Scholar 

  17. Li, H., Liu, A.: Asymptotic stability analysis via indefinite Lyapunov functions and design of nonlinear impulsive control systems. Nonlinear Anal. Hybrid Syst. 38, 100936 (2020)

    Article  MATH  Google Scholar 

  18. Li, H., Wu, Y., Chen, M.: Adaptive fault-tolerant tracking control for discrete-time multiagent systems via reinforcement learning algorithm. IEEE Trans. Cybernet. 51(3), 1163–1174 (2021)

    Article  Google Scholar 

  19. Li, X., Shen, J., Rakkiyappan, R.: Persistent impulsive effects on stability of functional differential equations with finite or infinite delay. Appl. Math. Comput. 329, 14–22 (2018)

    MATH  Google Scholar 

  20. Li, X., Yang, X., Huang, T.: Persistence of delayed cooperative models: impulsive control method. Appl. Math. Comput. 342, 130–146 (2019)

    MATH  Google Scholar 

  21. Li, X., Yang, X., Song, S.: Lyapunov conditions for finite-time stability of time-varying time-delay systems. Automatica 103, 135–140 (2019)

    Article  MATH  Google Scholar 

  22. Li, X., Zhang, X., Song, S.: Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica 76, 378–382 (2017)

    Article  MATH  Google Scholar 

  23. Lin, G., Li, H., Ma, H., Yao, D., Lu, R.: Human-in-the-loop consensus control for nonlinear multi-agent systems with actuator faults. IEEE/CAA J. Autom. Sin. 9(1), 111–122 (2022)

    Article  Google Scholar 

  24. Lin, H., Zeng, H., Wang, W.: New Lyapunov–Krasovskii functional for stability analysis of linear systems with time-varying delay. J. Syst. Sci. Complex. 34(2), 632–641 (2021)

    Article  MATH  Google Scholar 

  25. Liu, Y., Liu, X., Jing, Y., Wang, H., Li, X.: Annular domain finite-time connective control for large-scale systems with expanding construction. IEEE Trans. Syst. Man Cybernet. Syst. 51(10), 6159–6169 (2021)

    Article  Google Scholar 

  26. Miaadi, F., Li, X.: Impulse-dependent settling-time for finite time stabilization of uncertain impulsive static neural networks with leakage delay and distributed delays. Math. Comput. Simul. 182, 259–276 (2021)

    Article  MATH  Google Scholar 

  27. Ouyang, D., Shao, J., Jiang, H., Nguang, S.K., Shen, H.T.: Impulsive synchronization of coupled delayed neural networks with actuator saturation and its application to image encryption. Neural Netw. 128, 158–171 (2020)

    Article  MATH  Google Scholar 

  28. Tan, J., Li, C.: Finite-time stability of neural networks with impulse effects and time-varying delay. Neural Process. Lett. 46(1), 29–39 (2017)

    Article  Google Scholar 

  29. Tzan, S.R., Pantelides, C.P.: Convex models for impulsive response of structures. J. Eng. Mech. 122(6), 521–529 (1996)

    Google Scholar 

  30. Vrabel, R.: Criterion for robustness of global asymptotic stability to external perturbations of linear time-varying systems. Int. J. Gen. Syst. 50(2), 211–222 (2021)

    Article  Google Scholar 

  31. Wang, F., Chen, B., Sun, Y., Gao, Y., Lin, C.: Finite-time fuzzy control of stochastic nonlinear systems. IEEE Trans. Cybernet. 50(6), 2617–2626 (2020)

    Article  Google Scholar 

  32. Weiss, L., Infante, E.: Finite time stability under perturbing forces and on product spaces. IEEE Trans. Autom. Control 12(1), 54–59 (1967)

    Article  MATH  Google Scholar 

  33. Xi, Q., Liang, Z., Li, X.: Uniform finite-time stability of nonlinear impulsive time-varying systems. Appl. Math. Model. 91, 913–922 (2021)

    Article  MATH  Google Scholar 

  34. Xie, R., Li, C.: Stability analysis on Cohen–Grossberg neural networks with saturated impulse inputs. Neural Process. Lett. 51(2), 1265–1283 (2020)

    Article  Google Scholar 

  35. Yang, D., Li, X., Qiu, J.: Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback. Nonlinear Anal. Hybrid Syst. 32, 294–305 (2019)

    Article  MATH  Google Scholar 

  36. Yang, T.: Impulsive control theory—preface. Impulsive Control Theory 272, VII (2001)

    Google Scholar 

  37. Yang, Z., Zhang, J., Hu, J., Mei, J.: New results on finite-time stability for fractional-order neural networks with proportional delay. Neurocomputing 442, 327–336 (2021)

  38. You, L., Li, C., Han, Y.: Consensus of nonlinear multi-agent systems with fuzzy modelling uncertainties via state-constraint hybrid impulsive protocols. Int. J. Mach. Learn. Cybern. 11(12), 2653–2664 (2020)

  39. Zhang, X., Feng, G., Sun, Y.: Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems. Automatica 48(3), 499–504 (2012)

  40. Zhou, B.: Finite-time stabilization of linear systems by bounded linear time-varying feedback. Automatica 113, 108760 (2020)

    Article  MATH  Google Scholar 

Download references

Funding

This work was supported by the National Key Research and Development Project (2018AAA0100101) and the National Natural Science Foundation of P.R. China (Grant Nos. 61873213).

Author information

Authors and Affiliations

  1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, People’s Republic of China

    Runting Gan & Chuandong Li

Authors
  1. Runting Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuandong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chuandong Li.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gan, R., Li, C. Finite-time stability of nonlinear time-varying systems with saturated impulse inputs. Nonlinear Dyn 111, 3497–3507 (2023). https://doi.org/10.1007/s11071-022-08024-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-08024-y

Keywords

Search

Navigation