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Controllability, observability and fractional linear-quadratic problem for fractional linear systems with conformable fractional derivatives and some applications

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Abstract

In the present paper, we investigate the controllability, observability and fractional linear-quadratic problem of a non-homogeneous continuous-time fractional dynamical system (CF-DS) using the conformable fractional derivatives (CFD). We show that the controllability is equivalent to a controllability matrix that has a full rank. We also show a relationship between controllability and fractional differential Lyapunov equation. We give some theorems for observability of continuous-time fractional dynamical system. Moreover, we found a relationship between the solution of conformable fractional differential Riccati matrix equation and the solution of another conformable fractional linear system. We also find an optimal control that minimizes a functional cost under a conformable fractional system CF-DS by using the solution of fractional differential Riccati equation. Finally, we offer some applications to illustrate the effectiveness of our results.

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Acknowledgements

The authors should express their deep-felt thanks to the anonymous referees for their encouraging and constructive comments, which improved this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco

    Lakhlifa Sadek & Hamad Talibi Alaoui

  2. LabSIPE, National School of Applied Sciences of El Jadida, Chouaib Doukkali University, El Jadida, Morocco

    Bouchra Abouzaid & El Mostafa Sadek

Authors
  1. Lakhlifa Sadek
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  2. Bouchra Abouzaid
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  3. El Mostafa Sadek
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  4. Hamad Talibi Alaoui
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Correspondence to Lakhlifa Sadek.

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Sadek, L., Abouzaid, B., Sadek, E.M. et al. Controllability, observability and fractional linear-quadratic problem for fractional linear systems with conformable fractional derivatives and some applications. Int. J. Dynam. Control 11, 214–228 (2023). https://doi.org/10.1007/s40435-022-00977-7

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  • DOI: https://doi.org/10.1007/s40435-022-00977-7

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