An Integral and MRAC–Based Approach to the Adaptive Stabilisation of a Class of Linear Time–Delay Systems with Unknown Parameters

1Aguilar-Ibañez, C., García-Canseco, E. and Suárez-Castañón, M.S. (2013). Control adaptable basado en inmersión e invarianza (I&I) de una clase de sistemas lineales de segundo orden con parámetros desconocidos, Congreso Nacional de Control Automático (CNCA), Ensenada, Baja California Sur, Mexico, pp. 56–61.Search in Google Scholar

2Aguilar-Ibañez, C., Saldivar, B., Jiménez-Lizarraga, M., García-Canseco, E. and Garrido, R. (2021). Parametric uncertain second-order linear system output-adaptive stabilization: An integral and MRCA based approach, European Journal of Control 57: 76–81.Search in Google Scholar

3Ali, A.K. and Mahmoud, M.M. (2022). Improved design of nonlinear control systems with time delay, International Journal of Robotics and Control Systems 2(2): 317–331.Search in Google Scholar

4Åström, K.J. and Wittenmark, B. (2008). Adaptive Control, 2nd Edn, Dover Publications, Inc., Mineola.Search in Google Scholar

5Bekcheva, M., Mounier, H. and Greco, L. (2017). Control of differentially flat linear delay systems with constraints, IFAC-PapersOnLine 50(1): 13348–13353.Search in Google Scholar

6Bresch-Pietri, D., Chauvin, J. and Petit, N. (2012). Adaptive control scheme for uncertain time-delay systems, Automatica 48(8): 1536–1552.Search in Google Scholar

7Evesque, S., Annaswamy, A., Niculescu, S. and Dowling, A. (2003). Adaptive control of a class of time-delay systems, Journal of Dynamic Systems, Measurement and Control 125(2): 186–193.Search in Google Scholar

8Fang, M. and Park, J. (2013). A multiple integral approach to stability of neutral time-delay systems, Applied Mathematics and Computation 224: 714–718.Search in Google Scholar

9Gu, K., Kharitonov, V.L. and Chen, J. (2003). Stability of Time-Delay Systems, Birkh¨auser, New York.Search in Google Scholar

10Hua, C., Sun, Z. and Chen, Z. (2022). Stabilization for time-delay nonlinear systems with unknown time-varying control coefficients, Journal of the Franklin Institute 359(16): 8895–8909.Search in Google Scholar

11Jia, X., Xu, S., Lu, J., Li, Y., Chu, Y. and Zhang, Z. (2018). Adaptive control for uncertain nonlinear time-delay systems in a lower-triangular form, Journal of the Franklin Institute 355(9): 3911–3925.Search in Google Scholar

12Mathiyalagan, K. and Sangeetha, G. (2019). Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control, Journal of the Franklin Institute 356(7): 3948–3964.Search in Google Scholar

13Mera, M., Castanos, F. and Poznyak, A. (2014). Quantised and sampled output feedback for nonlinear systems, International Journal of Control 87(12): 2475–2487.Search in Google Scholar

14Mirkin, B. and Gutman, P.-O. (2010). Lyapunov-based adaptive output-feedback control of MIMO nonlinear plants with unknown, time-varying state delays, IFAC Proceedings Volumes 43(2): 33–38.Search in Google Scholar

15Mirkin, B.M. and Gutman, P.-O. (2005). Output feedback model reference adaptive control for multi-input–multi-output plants with state delay, Systems & Control Letters 54(10): 961–972.Search in Google Scholar

16Mirkin, B., Mirkin, E.L. and Gutman, P.-O. (2008). Model reference adaptive control of nonlinear plant with dead time, 2008 47th IEEE Conference on Decision and Control, Cancún, Quintana Roo, Mexico, pp. 1920–1924.Search in Google Scholar

17Nguyen, K.D. (2018). A predictor-based model reference adaptive controller for time-delay systems, IEEE Transactions on Automatic Control 63(12): 4375–4382.Search in Google Scholar

18Niculescu, S.-I. and Annaswamy, A.M. (2003). An adaptive smith-controller for time-delay systems with relative degree n∗ ≤ 2, Systems & Control Letters 49(5): 347–358.Search in Google Scholar

19Orlov, Y., Belkoura, L., Richard, J.-P. and Dambrine, M. (2003). Adaptive identification of linear time-delay systems, International Journal of Robust and Nonlinear Control: IFACAffiliated Journal 13(9): 857–872.Search in Google Scholar

20Orlov, Y., Kolmanovsky, I. and Gomez, O. (2009). Adaptive identification of linear time-delay systems: From theory toward application to engine transient fuel identification, International Journal of Adaptive Control and Signal Processing 23(2): 150–165.Search in Google Scholar

21Ortega, R., Hsu, L. and Astolfi, A. (2003). Immersion and invariance adaptive control of linear multivariable systems, Systems & Control Letters 49(1): 37–47.Search in Google Scholar

22Phoojaruenchanachai, S., Uahchinkul, K. and Prempraneerach, Y. (1998). Robust stabilisation of a state delayed system, IEEE Proceedings—Control Theory and Applications 145(1): 87–91.Search in Google Scholar

23Yao, D., Li, J. and Wu, J. (2019). Adaptive control design with assigned tracking accuracy for a class of nonlinearly parameterized input-delayed systems, Mathematical Problems in Engineering 2019, Article ID: 8602719.Search in Google Scholar

24Yuan, S., Zhang, L. and Baldi, S. (2019). Adaptive stabilization of impulsive switched linear time-delay systems: A piecewise dynamic gain approach, Automatica 103: 322–329.Search in Google Scholar

25Yuan, S., Zhang, L., Zhang, F., Wan, Y. and Baldi, S. (2018). Robust adaptive stabilization of switched higher-order planar nonlinear systems with unknown time-varying delays, IEEE International Conference on Systems, Man, and Cybernetics (SMC), Miyazaki, Japan, pp. 3249–3254.Search in Google Scholar