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Output feedback stabilization for high-order uncertain feedforward time-delay nonlinear systems. (English) Zbl 1395.93486

Summary: This paper addresses the output feedback stabilization problem for a class of high-order uncertain feedforward time-delay nonlinear systems. Under a weaken assumption that the powers of nonlinear functions are relaxed to an interval, the new control strategy implanting sign functions into homogeneous domination idea and observer construction allows time-varying delays to coexist in system state and control input. With the aid of delicate selections of design parameters, observer gains and Lyapunov-Krasovskii functionals, it is shown that the closed-loop system is globally asymptotically stable.

MSC:

93D15 Stabilization of systems by feedback
93C41 Control/observation systems with incomplete information
93C10 Nonlinear systems in control theory
93C20 Control/observation systems governed by partial differential equations
93D20 Asymptotic stability in control theory
Full Text: DOI

References:

[1] Qian, C.; Lin, W., Recursive observer design, homogeneous approximation, and nonsmooth output feedback stabilization of nonlinear systems, IEEE Trans. Autom. Control, 51, 9, 1457-1471, (2006) · Zbl 1366.93523
[2] Polendo, J.; Qian, C., A generalized homogeneous approach for global stabilization of inherently nonlinear systems via output feedback, Int. J. Robust Nonlinear Control, 17, 7, 605-629, (2007) · Zbl 1113.93087
[3] Sun, Z.; Liu, Y., Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems, Automatica, 43, 10, 1772-1783, (2007) · Zbl 1119.93061
[4] Yan, X.; Liu, Y., Global practical tracking for high-order uncertain nonlinear systems with unknown control directions, SIAM J. Control Optim., 48, 7, 4453-4473, (2010) · Zbl 1210.93035
[5] Li, W.; Jing, Y.; Zhang, S., Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable, Automatica, 46, 4, 752-760, (2010) · Zbl 1193.93146
[6] Du, H.; Qian, C.; Yang, S.; Li, S., Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems, Automatica, 49, 2, 601-609, (2013) · Zbl 1259.93029
[7] Sun, Z.; Zhang, X.; Xie, X., Global continuous output-feedback stabilization for a class of high-order nonlinear systems with multiple time delays, J. Frankl. Inst., 351, 8, 4334-4356, (2014) · Zbl 1294.93070
[8] Sun, Z.; Liu, Z.; Zhang, X., New results on global stabilization for time-delay nonlinear systems with low-order and high-order growth conditions, Int. J. Robust Nonlinear Control, 25, 6, 878-899, (2015) · Zbl 1309.93123
[9] Sepulchre, R.; Jankovic, M.; Kokotovic, P., Constructive nonlinear control, (1997), Springer New York · Zbl 1067.93500
[10] Isidori, A., Nonlinear control systems, (1999), Springer London · Zbl 0924.93038
[11] Ye, X., Universal stabilization of feedforward nonlinear systems, Automatica, 39, 1, 141-147, (2003) · Zbl 1010.93080
[12] Qian, C.; Li, J., Global output feedback stabilization of upper-triangular nonlinear systems using a homogeneous approach, Int. J. Robust Nonlinear Control, 16, 9, 441-463, (2006) · Zbl 1123.93081
[13] Ding, S.; Qian, C.; Li, S., Global stabilization of a class of feedforward systems with lower-order nonlinearities, IEEE Trans. Autom. Control, 55, 3, 691-696, (2010) · Zbl 1368.93532
[14] Ding, S.; Li, S.; Zheng, W., Nonsmooth stabilization of a class of nonlinear cascaded systems, Automatica, 48, 10, 2597-2606, (2012) · Zbl 1271.93116
[15] Hale, J.; Lunel, S., Introduction to functional differential equations, (1993), Springer-Verlag New York · Zbl 0787.34002
[16] Erneux, T., Applied delay differential equations, (2009), Springer-Verlag New York · Zbl 1201.34002
[17] Zhang, X.; Baron, L.; Liu, Q.; Boukas, E., Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems, IEEE Trans. Autom. Control, 56, 3, 692-697, (2011) · Zbl 1368.93587
[18] Zhang, X.; Liu, Q.; Baron, L.; Boukas, E., Feedback stabilization for high order feedforward nonlinear time-delay systems, Automatica, 47, 5, 962-967, (2011) · Zbl 1233.93079
[19] Zha, W.; Zhai, J.; Fei, S., Global output feedback control for a class of high-order feedforward nonlinear systems with input delay, ISA Trans., 52, 4, 494-500, (2013)
[20] Zhao, C.; Xie, X., Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay, Automatica, 50, 1, 203-210, (2014) · Zbl 1298.93351
[21] Balachandran, K., Controllability of nonlinear systems with delays in both state and control variables, Kybernetika, 22, 4, 340-348, (1986) · Zbl 0605.93009
[22] Zheng, G.; Barbot, J.; Boutat, D., On observation of time-delay systems with unknown inputs, IEEE Trans. Autom. Control, 56, 8, 1973-1978, (2011) · Zbl 1368.93068
[23] Califano, C.; Li, S.; Moog, C., Controllability of driftless nonlinear time-delay systems, Syst. Control Lett., 62, 3, 294-301, (2013) · Zbl 1261.93014
[24] Khalil, H. K., Nonlinear systems, (2002), Prentice Hall New Jersey · Zbl 1003.34002
[25] W. Ai, J. Zhai, S. Fei, Global output feedback stabilization for a class of stochastic feedforward nonlinear systems with time-varying input delay, Trans. Inst. Meas. Control (2015), http://dx.doi.org/10.1177/0142331214568238. · Zbl 1333.93196
[26] Sun, Z.; Xue, L.; Zhang, K., A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system, Automatica, 58, 8, 60-66, (2015) · Zbl 1330.93208
[27] Zhai, J., Finite-time output feedback stabilization for stochastic high-order nonlinear systems, Circuits Syst. Signal Process., 33, 12, 3809-3837, (2014) · Zbl 1342.93118
[28] Zhai, J.; Du, H., Global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems, Int. J. Control, 87, 10, 2106-2117, (2014) · Zbl 1308.93216
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