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Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay

IMEN Akrouti1, NADHEM Echi2   

  1. 1. Faculty of Sciences of Gafsa, Department of Mathematics, Gafsa University, Zarroug Gafsa 2112, Tunisia;
    2. Faculty of Sciences of Sfax, Department of Mathematics, Sfax University, BP 1171 Sfax 3000, Tunisia
  • Received:2021-03-04 Revised:2021-08-05 Online:2022-11-25 Published:2022-12-23
  • Contact: NADHEM Echi,Email:nadhemechi_fsg@yahoo.fr,nadhem.echi@fsgf.u-gafsa.tn

IMEN Akrouti, NADHEM Echi. Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2029-2045.

This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances. In case there is no perturbation, the exponential convergence of the observer was confirmed. When external disturbances appear in the system, a separation principle is established, and the authors show that the closed loop system is exponentially practical stable. By choosing a suitable Lyapunov-Krasovskii functional, the authors derive new sufficient conditions to guarantee the exponential stability of the systems. Finally, a physical model is performed to prove the efficiency and applicability of the suggested approach.
[1] Rajamani R, Observers for Lipschitz nonlinear systems, IEEE Trans. Automat. Control, 1998, 43(3): 397–401.
[2] Hu G, Observers for one-sided lipschitz non-linear systems, IMA Journal of Mathematical Control and Information, 2006, 23(4): 395–401.
[3] Abbaszadeh M and Marquez H J, Nonlinear observer design for one-sided Lipschitz systems, Proc. American Control Conf., Baltimore, USA, 2010, 5284–5289.
[4] Zhang W, Su H, Liang Y, et al., Nonlinear observer design for one-sided Lipschitz systems: A linear matrix inequality approach, IET Contr. Theory Appl., 2012, 6(9): 1297–1303.
[5] Zhang W, Liang Y, Su H S, et al., LMI-based observer design for one-sided Lipschitz nonlinear systems, Proc. 30th Chinese Control Conference, Yantai, China, 2011, 256–260.
[6] El-Haiek B, EL Aiss H, Hmamed A, et al., Robust observer design of one-sided Lipschitz nonlinear systems, Annual American Control Conference, USA, June 27–29, 2018, 5250–5255.
[7] Huang J, Yu L, and Shi M J, Adaptive observer design for quasi-one-sided lipschitz nonlinear systems, Proceedings of 2017 Chinese Intelligent Systems Conference, 2017, 13–22.
[8] He S, Lyu W, and Liu F, Robust H∞ sliding mode controller design of a class of time-delayed discrete conic-type nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(2): 885–892.
[9] Lu G and Ho D, Robust H∞ observer for a class of nonlinear discrete systems with time delay and parameter uncertainties, IEEE Proceedings Control Theory Application, 2004, 151: 439–444.
[10] Zhang W, Su H, Su S, et al., Nonlinear H∞ observer design for one-sided Lipschitz systems, Neurocomputing, 2014, 145: 505–511.
[11] Dastaviz A and Binazadeh T, Simultaneous stabilization for a collection of uncertain time-delay systems using sliding-mode output feedback control, Int. J. Control, 2020, 93(9): 2135–2144.
[12] Echi N and Ghanmi B, Global rational stabilization of a class of nonlinear time-delay systems, Arch. Control Sci., 2019, 29: 259–278.
[13] Ekramian M, Ataei M, and Talebi S, Stability of nonlinear time-delay systems satisfying a quadratic constraint, Trans. Inst. Meas. Control, 2018, 40(3): 712–718.
[14] Yang Y, Lin C, Chen B, et al., Reduced-order observer design for a class of generalized Lipschitz nonlinear systems with time-varying delay, Appl. Math. Comput., 2018, 337: 267–280.
[15] Zhu Q and Hu G, Stability analysis for uncertain nonlinear time-daly systems with quasi-onesided Lipschitz condition, Acta Automat. Sinca, 2009, 35: 1006–1009.
[16] Zhang Z and Xu S, Observer design for uncertain nonlinear systems with unmodeled dynamics, Automatica, 2015, 51: 80–84.
[17] Echi N, Observer design and practical stability of nonlinear systems under unknown time-delay, Asian Journal of Control, 2021, 23(2): 685–696.
[18] Echi N and Benabdallah A, Obsever besed control for strong practical stabilization of a class of uncertain time delay systems, Kybernetika, 2020, 55(6): 1016–1033.
[19] Dong Y, Liu W, and Liang S, Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties, International Journal of Robust and Nonlinear Control, 2017, 27(11): 1974–1998.
[20] Asadinia M A and Binazadeh T, Finite-time stabilization of descriptor time-delay systems with one-sided Lipschitz nonlinearities: Application to partial element equivalent circuit, Circuits, Systems, and Signal Processing, 2019, 38(12): 5467–5487.
[21] Gholami H and Binazadeh T, Observer-based H finite-time controller for time-delay nonlinear one-sided Lipschitz systems with exogenous disturbances, J. Vib. Control, 2018, https://doi.org/10.1177/1077546318802422.
[22] Ahmad S, Majeed R, Hong K S, et al., Observer design for one-sided Lipschitz nonlinear systems subject to measurement delays, Mathematical Problems in Engineering, 2015, Article ID 879492, 13 pages, https://doi.org/10.1155/2015/879492.
[23] Nguyen M C and Trinh H, Reduced-order observer design for one-sided Lipschitz time-delay systems subject to unknown inputs, IET Control Theory Appl., 2016, 10(10): 1097–1105.
[24] Ellouze I, Separation principle of time-varying systems including multiple delayed perturbations, Bulletin des Sciences Mathématiques, 2020, 161(1): 102869.
[25] Ben Hamed B, Ellouze I, and Hammami M A, Practical uniform stability of nonlinear differential delay equation, Mediterranean Journal of Mathematics 2011, 8: 603–616.
[26] Benabdallah A and Echi N, Global exponential stabilisation of a class of nonlinear time-delay systems, International Journal of Systems Science, 2016, 47: 3857–3863.
[27] Echi N and Benabdallah A, Delay-dependent stabilization of a class of time-delay nonlinear systems: LMI approach, Advances in Difference Equations, 2017, 271, DOI: 10.1186/s13662-017-1335-7.
[28] Dong Y, Liu W, and Liang S, Reduced-order observer-based controller design for quasi-onesided Lipschitz nonlinear systems with time-delay, International Journal of Robust and Nonlinear Control, 2021, 31(3): 817–831.
[29] Hu G D, Dong W, and Cong Y, Separation principle for quasi-one-sided Lipschitz nonlinear systems with time-delay, Int. J. Robust Nonlinear Control, 2020, 30(6): 2430–2442.
[30] Liu P L, New results on stability analysis for time-varying delay systems with non-linear perturbations, ISA Transactions, 2013, 52: 318–325.
[31] Nie R, He S, Liu F, et al., Sliding mode controller design for conic-type nonlinear semi-Markovian jumping systems of time-delayed Chua’s circuit, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(4): 2467–2475.
[32] Cullum J, Ruehli A, and Zhang T, A method for reduced-order modeling and simulation of large interconnect circuits and its application to PEEC models with retardation, IEEE Trans. Circuits Syst. II Analog Digit. Signal Process, 2000, 47(4): 261–273.
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