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Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit

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  • Wang, Xuezhen
  • Zhang, Huasheng

Abstract

This paper investigates the variable convergence rate stability and variable convergence rate stabilization of impulsive dynamic linear systems with stabilizing impulses affected by nonlinear disturbances. The eigenvalues (poles) of the system state are closely related to the convergence or divergence rate of the system. Sufficient conditions for the variable convergence rate stability are obtained by using the generalized pole placement idea and the method of system transformation. By designing a memoryless state feedback controller, sufficient conditions of variable convergence rate stabilization are obtained, ensuring the asymptotic stability of the target closed-loop system and accurately adjusting the system state’s convergence rate. An algorithm for adjusting the speed of system state convergence and its flow chart are designed by referring to the C programming language. Combined with the variable convergence rate stabilization method, the intelligent control of system state convergence speed is realized at the operation level. As a representative example of chaotic systems, Chua’s circuit affected by impulses verifies the effectiveness of the variable convergence rate stabilization method.

Suggested Citation

  • Wang, Xuezhen & Zhang, Huasheng, 2023. "Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s096007792300190x
    DOI: 10.1016/j.chaos.2023.113289
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    References listed on IDEAS

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    1. Usama, B.I. & Morfu, S. & Marquie, P., 2021. "Vibrational resonance and ghost-vibrational resonance occurrence in Chua’s circuit models with specific nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Yang, Feifei & Ma, Jun & An, Xinlei, 2022. "Mode selection and stability of attractors in Chua circuit driven by piezoelectric sources," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Lakshmi Priya, P.K. & Kaliraj, K., 2022. "An application of fixed point technique of Rothe’s-type to interpret the controllability criteria of neutral nonlinear fractional ordered impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Baolong Zhu & Jie Ma & Zhiping Zhang & Hui Feng & Shunli Li, 2018. "Robust stability analysis and stabilisation of uncertain impulsive positive systems with time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(14), pages 2940-2956, October.
    5. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Wang, Zhixiang & Zhang, Chun & Bi, Qinsheng, 2022. "Bursting oscillations with bifurcations of chaotic attractors in a modified Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    7. Xuan, Deli & Tang, Ze & Feng, Jianwen & Park, Ju H., 2021. "Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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    Cited by:

    1. Li, Yuanen & Zhang, Huasheng & Xie, Xiangpeng & Xia, Jianwei, 2023. "Stability analysis of a cart-pendulum model with variable convergence rate: A sliding mode control approach for impulsive stochastic systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Remus-Daniel Ene & Nicolina Pop, 2023. "Semi-Analytical Closed-Form Solutions for the Rikitake-Type System through the Optimal Homotopy Perturbation Method," Mathematics, MDPI, vol. 11(14), pages 1-22, July.

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