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observer; exponential stability; strong practical stability; time delay; Lyapunov--Krasovskii
In this paper, we address the strong practical stabilization problem for a class of uncertain time delay systems with a nominal part written in triangular form. We propose, firstly, a strong practical observer. Then, we show that strong practical stability of the closed loop system with a linear, parameter dependent, state feedback is achieved. Finally, a separation principle is established, that is, we implement the control law with estimate states given by the strong practical observer and we prove that the closed loop system is strong practical stable. With the help of a numerical example, effectiveness of the proposed approach is demonstrated.
[1] J., Anthonis,, A., Seuret,, J.-.P., Richard,, H., Ramon,: Design of a pressure control system with band time delay.
[2] A., Atassi,, K., Khalil, H.: A separation principle for the stabilization of a class of nonlinear systems. IEEE Trans. Automat. Control 44 (1999), 1672-1687. DOI 10.1109/9.788534 | MR 1709863 | Zbl 0958.93079
[3] A., Atassi,, K., Khalil, H.: Separation results for the stabilization of nonlinear systems using different high-gain observer designs. Systems Control Lett. 39 (2000), 183-191. DOI 10.1016/S0167-6911(99)00085-7 | MR 1831258 | Zbl 0948.93007
[4] A., Benabdallah,: A separation principle for the stabilization of a class of time delay nonlinear systems. Kybernetika 51 ( 2015 ), 99-111. DOI 10.14736/kyb-2015-1-0099 | MR 3333835
[5] A., Benabdallah,, N., Echi,: Global exponential stabilisation of a class of nonlinear time-delay systems. Int. J. Systems Sci. 47 (2016), 3857-3863. DOI 10.1080/00207721.2015.1135356 | MR 3512589
[6] A., Benabdallah,, I., Ellouze,, A., Hammami, M.: Practical exponential stability of perturbed triangular systems and separation principle.
[7] A., Benabdallah,, I., Ellouze,, A., Hammami, M.: Practical stability of nonlinear time-varying cascade systems.
[8] A., Benabdallah,, T., Kharrat,, C., Vivalda, J.: On practical observers for nonlinear uncertain systems. Systems Control Lett. 57 (2008), 371-377. DOI 10.14736/kyb-2015-1-0099 | MR 2405104
[9] Y., Dong,, X., Wang,, S., Mei,, W., Li,: Exponential stabilization of nonlinear uncertain systems with time-varying delay. J. Engrg. Math. 77 (2012), 225-237. DOI 10.1007/s10665-012-9554-0 | MR 2990665
[10] N., Echi,: Observer design and practical stability of nonlinear systems under unknown time-delay. Asian J. Control (2019). DOI
[11] N., Echi,, A., Benabdallah,: Delay-dependent stabilization of a class of time-delay nonlinear systems: LMI approach. Adv. Differ. Equ. 271 (2017), 1-13. DOI 10.1186/s13662-017-1335-7 | MR 3695397
[12] N., Echi,, B., Ghanmi,: Global rational stabilization of a class of nonlinear time-delay systems. Arch. Control Sci. 29 (2019), 259-278. DOI 10.24425/acs.2019.129381 | MR 4033936
[13] B., Hamed,, I., Ellouze,, A., Hammami, M.: Practical uniform stability of nonlinear differential delay equation. Mediterr. J. Math. 8 (2011), 603-616. DOI 10.1007/s00009-010-0083-7 | MR 2860688
[14] B., Hamed,, A., Hammami, M.: Practical stabilization of a class of uncertain time-varying nonlinear delay systems. J. Control Theory Appl. 7 (2009), 175-180. DOI 10.1007/s11768-009-8017-2 | MR 2526947
[15] M., Farza,, A., Sboui,, E., Cherrier,, M., M'Saad,: High-gain observer for a class of time-delay nonlinear systems. Int. J. Control 83 (2010), 273-280. DOI 10.1080/00207170903141069 | MR 2606182
[16] A., Germani,, C., Manes,, P., Pepe,: An asymptotic state observer for a class of nonlinear delay systems.
[17] A., Germani,, C., Manes,, P., Pepe,: Local asymptotic stability for nonlinear state feedback delay systems. Kybernetika 36 (2000), 31-42. MR 1760886 | Zbl 1249.93146
[18] A., Germani,, C., Manes,, P., Pepe,: Observer-based stabilizing control for a class of nonlinear retarded systems. Lect. Notes Control Inform. Sci. 423 (2012), 331-342. DOI 10.1007/978-3-642-25221-1_25 | MR 3050770 | Zbl 1298.93287
[19] M., Ghanes,, De, Leon, J., J., Barbot,: Observer design for nonlinear systems under unknown time-varying delays. IEEE Trans. Automat. Control 58 (2013), 1529-1534. DOI 10.1109/TAC.2012.2225554 | MR 3065135
[20] K., Hale, J., V., Lunel, S. M.: Introduction to Functional Differential Equations. Springer, New York 1993. MR 1243878 | Zbl 0787.34002
[21] S., Ibrir,: Observer-based control of a class of time-delay nonlinear systems having triangular structure.
[22] X., Jia,, X., Chen,, S., Xu,, B., Zhang,, Z., Zhang,: Adaptive output feedback control of nonlinear time-delay systems with application to chemical reactor systems. IEEE Trans. Ind. Electron. 64 (2017), 4792-4799. DOI 10.1109/TIE.2017.2668996
[23] X., Jia,, S., Xu,, J., Chen,, Z., Li,, Y., Zou,: Global output feedback practical tracking for time-delay systems with uncertain polynomial growth rate. J. Franklin Inst. 352 (2015), 5551-5568. DOI 10.1016/j.jfranklin.2015.08.012 | MR 3428380
[24] X., Jia,, S., Xu,, J., Lu,, Y., Li,, Y., Chu,, Z., Zhang,: Adaptive control for uncertain nonlinear time-delay systems in a lower-triangular form.
[25] A., Koshkouei,, J., Burnham, K.: Discontinuous observers for non-linear time-delay systems. Int. J. Systems Sci. 40 (2009), 383-392. DOI 10.1080/00207720802439293 | MR 2510653
[26] M., Kwona, O., H., Parkb, J.: Exponential stability of uncertain dynamic systems including state delay.
[27] C., Lili,, Z., Ying,, Z., Xian,: Guaranteed cost control for uncertain genetic regulatory networks with interval time-varying delays. Neurocomputing 131 (2014), 105-112. DOI 10.1016/j.neucom.2013.10.035
[28] S., Mondal,, K., Chung, W.: Adaptive observer for a class of nonlinear systems with time-varying delays.
[29] S., Mondie,, L., Kharitonov, V.: Exponential estimates for retarded time delay systems: an LMI approach. IEEE Trans. Automat. Control 50 (2005), 268-273. DOI 10.1016/j.jmaa.2014.12.019 | MR 2116437
[30] Y., Muroya,, T., Kuniya,, L., Wang, J.: Stability analysis of a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure. J. Math. Anal. Appl. 425 (2015), 415-439. DOI doi | MR 3299671
[31] O., Naifar,, Ben, Makhlouf, A., A., Hammami, M., A., Ouali,: On Observer design for a class of nonlinear systems including unknown time-delay. Mediterr. J. Math. 13 (2016), 2841-2851. DOI 10.1007/s00009-015-0659-3 | MR 3554282
[32] P., Pepe,, I., Karafyllis,: Converse Lyapunov-Krasovskii theorems for systems described by neutral functional differential equations in Hales form. Int. J. Control 86 (2013), 232-243. DOI 10.1080/00207179.2012.723137 | MR 3017700
[33] A., Rapaport,, L., Gouze, J.: Parallelotopic and practical observers for non-linear uncertain systems. Int. J. Control 76 (2003), 237-251. DOI 10.1080/0020717031000067457 | MR 1984076
[34] R., Villafuerte,, S., Mondie,, A., Poznyak,: Practical stability of time-delay systems: LMI's approach. Eur. J. Control 2 (2011), 127-138. DOI 10.3166/ejc.17.127-138 | MR 2839109
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