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

Rajamani R, Observers for Lipschitz nonlinear systems, IEEE Trans. Automat. Control, 1998, 43(3): 397–401. Hu G, Observers for one-sided lipschitz non-linear systems, IMA Journal of Mathematical Control and Information, 2006, 23(4): 395–401. Abbaszadeh M and Marquez H J, Nonlinear observer design for one-sided Lipschitz systems, Proc. American Control Conf., Baltimore, USA, 2010, 5284–5289. 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. 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. 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. 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. 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. 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. Zhang W, Su H, Su S, et al., Nonlinear H∞ observer design for one-sided Lipschitz systems, Neurocomputing, 2014, 145: 505–511. 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. Echi N and Ghanmi B, Global rational stabilization of a class of nonlinear time-delay systems, Arch. Control Sci., 2019, 29: 259–278. 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. 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. 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. Zhang Z and Xu S, Observer design for uncertain nonlinear systems with unmodeled dynamics, Automatica, 2015, 51: 80–84. Echi N, Observer design and practical stability of nonlinear systems under unknown time-delay, Asian Journal of Control, 2021, 23(2): 685–696. 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. 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. 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. 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. 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. 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. Ellouze I, Separation principle of time-varying systems including multiple delayed perturbations, Bulletin des Sciences Mathématiques, 2020, 161(1): 102869. 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. 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. 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: https://doi.org/10.1186/s13662-017-1335-7. 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. 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. Liu P L, New results on stability analysis for time-varying delay systems with non-linear perturbations, ISA Transactions, 2013, 52: 318–325. 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. 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.