Research Article

LMI Approach for Asymptotical Stability of Riemann–Liouville Nonlinear Fractional Neutral Systems with Time-Varying Delays

Volume: 28 Number: 3 December 29, 2023
Erdal Korkmaz *, Abdulhamit Özdemir
PDF Download
Yuzuncu Yil University Journal of the Institute of Natural and Applied Sciences Cover Yuzuncu Yil University Journal of the Institute of Natural and Applied Sciences
TR EN

LMI Approach for Asymptotical Stability of Riemann–Liouville Nonlinear Fractional Neutral Systems with Time-Varying Delays

Abstract

In this paper, we have delivered asymptotic stability results for solutions to non-autonomous nonlinear neutral systems. The acquired stability results are independent of the delays, and the delays are also both time-variable and unbounded. Additionally, the results were described as a convex optimization problem, and an example was used to examine the results' feasibility and efficacy.

Keywords

Asymptotical stability , Convex optimization problem , Fractional neutral systems , Riemann-Liouville derivative

References

  1. Altun, Y., & Tunç, C. (2020). On the asymptotic stability of a nonlinear fractional-order system with multiple variable delays. Applications and Applied Mathematics, 15(1), 458-468.
  2. Chen, L. P., He, Y. G., Chai, Y., & Wu, R. C. (2014). New results on stability stabilization of a class of nonlinear fractional-order systems. Nonlinear Dynamics, 75, 633-641. doi:10.1007/s11071-013-1091-5
  3. Chen, L. P., Liu, C., Wu, R. C., He, Y. G., & Chai, Y. (2016). Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Computing and Applications, 27, 549-556. doi:10.1007/s00521-015-1876-1
  4. Deng, W. H., Li, C. P., & Lu, J. H. (2007). Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics, 48, 409-416. doi:10.1007/s11071-006-9094-0
  5. Duarte-Mermoud, M. A., Aguila-Camacho, N., Gallegos, J. A., & Castro-Linares, R. (2015). Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Communications in Nonlinear Science and Numerical Simulation, 22, 650-659. doi:10.1016/j.cnsns.2014.10.008
  6. Hale, J. (1977). Theory of Functional Differential Equations. New York, USA: Springer-Verlag.
  7. Heymans, N., & Podlubny, I. (2006). Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta, 45(5), 765-771. doi:10.1007/s00397-005-0043-5
  8. Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and Application of Fractional Differential Equations. New York, USA: Elsevier.
  9. Korkmaz, E., & Özdemir, A. (2019). On stability of fractional differential equations with Lyapunov functions. MAUN Fen Bilimleri Dergisi, 7(1), 635-638. doi:10.18586/msufbd.559400
  10. Li, H., Zhou, S., & Li, H. (2015). Asymptotic stability analysis of fractional-order neutral systems with time delay. Advances in Continuous and Discrete Models, 2015, 325-335

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Publication Date

December 29, 2023

Submission Date

February 2, 2023

Acceptance Date

June 19, 2023

Published in Issue

Year 2023 Volume: 28 Number: 3

DOI

https://doi.org/10.53433/yyufbed.1246729

IZ

https://izlik.org/JA96WF85GE

Cite

RIS / Bibtex
APA
Korkmaz, E., & Özdemir, A. (2023). LMI Approach for Asymptotical Stability of Riemann–Liouville Nonlinear Fractional Neutral Systems with Time-Varying Delays. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 28(3), 908-918. https://doi.org/10.53433/yyufbed.1246729