86
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Hierarchical conditions for exponential stabilisation of time-varying delay systems using Bessel–Legendre inequalities and Finsler's lemma

ORCID Icon
Pages 2337-2351 | Received 28 Feb 2023, Accepted 22 Jun 2023, Published online: 07 Jul 2023

References

  • Bajodek, M., Seuret, A., & Gouaisbaut, F. (2022). On the necessity of sufficient LMI conditions for time-delay systems arising from Legendre approximation. arXiv, arXiv:2207.08423, preprint.
  • Bourahala, F., Rouamel, M., & Guelton, K. (2021). Improved robust H∞ stability analysis and stabilization of uncertain systems with stochastic input time-varying delays. Optimal Control Applications and Methods, 42(5), 1512–1530. https://doi.org/10.1002/oca.v42.5
  • Chen, J., & Park, J. H. (2020). New versions of Bessel–Legendre inequality and their applications to systems with time-varying delay. Applied Mathematics and Computation, 375, 125060. https://doi.org/10.1016/j.amc.2020.125060
  • De Oliveira, F. S., & Souza, F. O. (2020). Further refinements in stability conditions for time-varying delay systems. Applied Mathematics and Computation, 369, 124866. https://doi.org/10.1016/j.amc.2019.124866
  • De Oliveira, M. C., & Skelton, R. E. (2001). Stability tests for constrained linear systems. In Perspectives in robust control (pp. 241–257). Springer-Verlag.
  • Gao, H., Chen, T., & Lam, J. (2008). A new delay system approach to network-based control. Automatica, 44(1), 39–52. https://doi.org/10.1016/j.automatica.2007.04.020
  • González, A. (2021). A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems. International Journal of Systems Science, 52(8), 1707–1718. https://doi.org/10.1080/00207721.2020.1869344
  • González, A. (2022). Improved results on stability analysis of time-varying delay systems via delay partitioning method and Finsler's lemma. Journal of the Franklin Institute, 359(14), 7632–7649. https://doi.org/10.1016/j.jfranklin.2022.07.032
  • Gu, K. (2001). A further refinement of discretized Lyapunov functional method for the stability of time-delay systems. International Journal of Control, 74(10), 967–976. https://doi.org/10.1080/00207170110047190
  • Gu, K., Chen, J., & Kharitonov, V. L. (2003). Stability of time-delay systems. Springer Science & Business Media.
  • Gyurkovics, É. (2015). A note on Wirtinger-type integral inequalities for time-delay systems. Automatica, 61, 44–46. https://doi.org/10.1016/j.automatica.2015.07.033
  • Hu, W., & Zhu, Q. (2020). Stability analysis of impulsive stochastic delayed differential systems with unbounded delays. Systems & Control Letters, 136, 104606. https://doi.org/10.1016/j.sysconle.2019.104606
  • Li, Z., Yan, H., Zhang, H., Peng, Y., Park, J. H., & He, Y. (2020). Stability analysis of linear systems with time-varying delay via intermediate polynomial-based functions. Automatica, 113, 108756. https://doi.org/10.1016/j.automatica.2019.108756
  • Lin, H., & Dong, J. (2023). Stability analysis of T–S fuzzy systems with time-varying delay via parameter-dependent reciprocally convex inequality. International Journal of Systems Science, 54(6), 1289–1298. https://doi.org/10.1080/00207721.2023.2172327
  • Liu, F., Liu, H., Li, Y., & Sidorov, D. (2023). Two relaxed quadratic function negative-determination lemmas: Application to time-delay systems. Automatica, 147, 110697. https://doi.org/10.1016/j.automatica.2022.110697
  • Liu, K., Seuret, A., & Xia, Y. (2017). Stability analysis of systems with time-varying delays via the second-order Bessel–Legendre inequality. Automatica, 76, 138–142. https://doi.org/10.1016/j.automatica.2016.11.001
  • Long, F., Zhang, C. K., He, Y., Wang, Q. G., & Wu, M. (2021). A sufficient negative-definiteness condition for cubic functions and application to time-delay systems. International Journal of Robust and Nonlinear Control, 31(15), 7361–7371. https://doi.org/10.1002/rnc.v31.15
  • Mátyás, A., Nagy, Z., & Lendek, Z. (2020). Controller design for time-delay TS fuzzy systems with nonlinear consequents. In 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (pp. 1–6). Glasgow, UK: IEEE, Conference.
  • Park, J., & Park, P. (2020). Finite-interval quadratic polynomial inequalities and their application to time-delay systems. Journal of the Franklin Institute, 357(7), 4316–4327. https://doi.org/10.1016/j.jfranklin.2020.01.022
  • Park, P., Ko, J. W., & Jeong, C. (2011). Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 47(1), 235–238. https://doi.org/10.1016/j.automatica.2010.10.014
  • Park, P., Lee, W. I., & Lee, S. Y. (2015). Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. Journal of the Franklin Institute, 352(4), 1378–1396. https://doi.org/10.1016/j.jfranklin.2015.01.004
  • Parlakçı, M. A. (2006). Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time-delay systems. International Journal of Robust and Nonlinear Control, 16(13), 599–636. https://doi.org/10.1002/(ISSN)1099-1239
  • Phat, V., Khongtham, Y., & Ratchagit, K. (2012). LMI approach to exponential stability of linear systems with interval time-varying delays. Linear Algebra and its Applications, 436(1), 243–251. https://doi.org/10.1016/j.laa.2011.07.016
  • Qiu, Y., Hua, C., Park, J. H., & Wang, Y. (2023). Interval approximation method for stability analysis of time-delay systems. Journal of the Franklin Institute, 360(4), 3034–3046. https://doi.org/10.1016/j.jfranklin.2022.12.056
  • Rajendra Prasad, K., Arun, N., & Venkatesh, M. (2022). An improved stabilization criteria for linear systems with time-varying delay using a new Lyapunov–Krasovskii functional. In Control and measurement applications for smart grid (pp. 335–346). Springer.
  • Selivanov, A., & Fridman, E. (2016). Predictor-based networked control under uncertain transmission delays. Automatica, 70, 101–108. https://doi.org/10.1016/j.automatica.2016.03.032
  • Seuret, A., & Gouaisbaut, F. (2013). Wirtinger-based integral inequality: Application to time-delay systems. Automatica, 49(9), 2860–2866. https://doi.org/10.1016/j.automatica.2013.05.030
  • Seuret, A., & Gouaisbaut, F. (2015). Hierarchy of LMI conditions for the stability analysis of time-delay systems. Systems & Control Letters, 81, 1–7. https://doi.org/10.1016/j.sysconle.2015.03.007
  • Seuret, A., & Gouaisbaut, F. (2017). Stability of linear systems with time-varying delays using Bessel–Legendre inequalities. IEEE Transactions on Automatic Control, 63(1), 225–232. https://doi.org/10.1109/TAC.2017.2730485
  • Sun, J., Liu, G., & Chen, J. (2009). Delay-dependent stability and stabilization of neutral time-delay systems. International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal, 19(12), 1364–1375. https://doi.org/10.1002/rnc.v19:12
  • Sun, Y., & Xie, X. J. (2020). Stability analysis of nonlinear time-varying systems with bounded and unbounded delays. Journal of the Franklin Institute, 357(11), 6968–6978. https://doi.org/10.1016/j.jfranklin.2020.04.053
  • Tian, Y., & Wang, Z. (2021). Composite slack-matrix-based integral inequality and its application to stability analysis of time-delay systems. Applied Mathematics Letters, 120, 107252. https://doi.org/10.1016/j.aml.2021.107252.
  • Tian, Y., & Wang, Z. (2022). Stability analysis of linear time-varying system via flexible polynomial-based functions. International Journal of Systems Science, 53(2), 402–411. https://doi.org/10.1080/00207721.2021.1958026
  • Venkatesh, M., Patra, S., & Ray, G. (2018). Stabilization of uncertain linear system with time-varying delay using a new Lyapunov–Krasovskii functional. In IEEE Region 10th Conference (TENCON 2018) (pp. 205–210). Jeju, Korea (South): IEEE, Conference.
  • Wang, Y., Hua, C., Park, P., & Qian, C. (2023). Stability criteria for time-varying delay systems via an improved reciprocally convex inequality lemma. Applied Mathematics and Computation, 448(2023), 127918. https://doi.org/10.1016/j.amc.2023.127918
  • Zeng, H. B., Lin, H. C., He, Y., Teo, K. L., & Wang, W. (2020). Hierarchical stability conditions for time-varying delay systems via an extended reciprocally convex quadratic inequality. Journal of the Franklin Institute, 357(14), 9930–9941. https://doi.org/10.1016/j.jfranklin.2020.07.034
  • Zeng, H. B., Liu, X. G., & Wang, W. (2019). A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems. Applied Mathematics and Computation, 354, 1–8. https://doi.org/10.1016/j.amc.2019.02.009
  • Zeng, H. B., Zhai, Z. L., & Wang, W. (2021). Hierarchical stability conditions of systems with time-varying delay. Applied Mathematics and Computation, 404, 126222. https://doi.org/10.1016/j.amc.2021.126222
  • Zhang, X. M., Han, Q. L., & Ge, X. (2022). The construction of augmented Lyapunov–Krasovskii functionals and the estimation of their derivatives in stability analysis of time-delay systems: A survey. International Journal of Systems Science, 53(12), 2480–2495. https://doi.org/10.1080/00207721.2021.2006356

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.