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Controllability of fractional damped dynamical systems

Author

Listed:
  • Balachandran, K.
  • Govindaraj, V.
  • Rivero, M.
  • Trujillo, J.J.

Abstract

In this paper, we study the controllability of linear and nonlinear fractional damped dynamical systems, which involve fractional Caputo derivatives, with different order in finite dimensional spaces using the Mittag–Leffler matrix function and the iterative technique. A numerical example is provided to illustrate the theory.

Suggested Citation

  • Balachandran, K. & Govindaraj, V. & Rivero, M. & Trujillo, J.J., 2015. "Controllability of fractional damped dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 66-73.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:66-73
    DOI: 10.1016/j.amc.2014.12.059
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    References listed on IDEAS

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    1. Narahari Achar, B.N. & Hanneken, John W. & Clarke, T., 2002. "Response characteristics of a fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 275-288.
    2. K. Balachandran & V. Govindaraj & L. Rodríguez-Germa & J. J. Trujillo, 2013. "Controllability Results for Nonlinear Fractional-Order Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 33-44, January.
    3. Achar, B.N.Narahari & Hanneken, J.W. & Enck, T. & Clarke, T., 2001. "Dynamics of the fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 361-367.
    4. Tofighi, Ali, 2003. "The intrinsic damping of the fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 29-34.
    5. Stanislavsky, Aleksander A., 2005. "Twist of fractional oscillations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 101-110.
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    Cited by:

    1. Cao, Yueju & Sun, Jitao, 2017. "Controllability of measure driven evolution systems with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 119-126.
    2. Jiale Sheng & Wei Jiang & Denghao Pang & Sen Wang, 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    3. Arthi, G. & Park, Ju H. & Suganya, K., 2019. "Controllability of fractional order damped dynamical systems with distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 74-91.
    4. Kumar, Vipin & Malik, Muslim & Debbouche, Amar, 2021. "Stability and controllability analysis of fractional damped differential system with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    5. Zhang, Tao & Lu, Zhong-rong & Liu, Ji-ke & Chen, Yan-mao & Liu, Guang, 2023. "Parameter estimation of linear fractional-order system from laplace domain data," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    6. Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Wang, JinRong & Fĕckan, Michal & Zhou, Yong, 2017. "Center stable manifold for planar fractional damped equations," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 257-269.
    8. Tian, Xue & Zhang, Yi, 2021. "Fractional time-scales Noether theorem with Caputo Δ derivatives for Hamiltonian systems," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    9. Wang, Zhi-Bo & Liu, Da-Yan & Boutat, Driss, 2022. "Algebraic estimation for fractional integrals of noisy acceleration based on the behaviour of fractional derivatives at zero," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    10. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.
    11. Arthi, G. & Suganya, K., 2021. "Controllability of higher order stochastic fractional control delay systems involving damping behavior," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    12. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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