Compensation problem in linear fractional order disturbed systems

    Chadi Amissi   Affiliation
    ; El Mostafa Magri   Affiliation
    ; Mustapha Lhous   Affiliation
    ; Larbi Afifi   Affiliation


In this paper, we study fractional-order linear, finite-dimensional disturbed systems. The fundamental objective of this work is to study the remediability or compensation problem in linear fractional-order time-invariant perturbed systems. The remediability was introduced with the aim of finding an appropriate control that steers the output of the perturbed system towards normal observation at the final moment. We begin first by giving some characterizations of compensation, and then we prove that a rank condition is sufficient to assure the remediability of our system. The relationship between controllability and compensation is also given, and we provide some examples to illustrate our results.

Keyword : fractional order, disturbed systems, controllability, remediability, observation

How to Cite
Amissi, C., Magri, E. M., Lhous, M., & Afifi, L. (2024). Compensation problem in linear fractional order disturbed systems. Mathematical Modelling and Analysis, 29(3), 546–559.
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Jun 27, 2024
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L. Afifi, M. El Mostafa and J. Abdelhaq. Compensation problem in flnite dimension linear dynamical systems. International Journal of Applied Mathematical Sciences, 2(45):2219–2228, 2008.

L. Afifi, K. Lasri, M. Joundi and N. Amimi. Feedback controls for finite time or asymptotic compensation in lumped disturbed systems. Journal of Advances in Mathematics and Computer Science, 7(3):168–180, 2015.

I. Ahmad, S. Ahmad, G. ur Rahman, S. Ahmad and M. De La Sen. Controllability and observability results of an implicit type fractional order delay dynamical system. Mathematics, 10(23):1–24, 2022.

L. Benahmadi, M. Lhous, A. Tridane and M. Rachik. Output trajectory controllability of a discrete-time sir epidemic model. Mathematical Modelling of Natural Phenomena, 18(16):1–18, 2023.

R.F. Curtain and A.J. Pritchard. Infinite Dimensional Linear Systems Theory. Springer Berlin, Heidelberg, 1978.

A. Larrache, M. Lhous, S. Ben Rhila, M. Rachik and A. Tridane. An output sensitivity problem for a class of linear distributed systems with uncertain initial state. Archives of Control Sciences, 30(1):39–155, 2020.

E.M. Magri, C. Amissi, L. Afifi and M. Lhous. On the minimum energy compensation for linear time-varying disturbed systems. Archives of Control Sciences, 32(4):733–754, 2022.

M. Mohan Raja, A. Shukla, J.J. Nieto, V. Vijayakumar and K.S. Nisar. A note on the existence and controllability results for fractional integrodifferential inclusions of order r ∈ (1;2] with impluses. Qualitative Theory of Dynamical Systems, 21(150), 2022.

S. Rekkab and S. Benhadid. Gradient remediability in linear distributed parabolic systems analysis, approximations and simulations. Journal of Fundamental and Applied Sciences, 9(3):1535–1558, 2017.

S. Souhail and L. Afifi. Cheap controls for disturbances compensation in hyperbolic delayed systems. International Journal of Dynamical Systems and Differential Equations, 10(6):511–536, 2020.