×

Global finite-time stabilization for a class of uncertain high-order nonlinear systems. (English) Zbl 1406.93270

Summary: This paper addresses the problem of global finite-time stabilization by state feedback for a class of high-order nonlinear systems under weaker condition. By using the methods of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee the global finite-time stability of the resulting closed-loop system. A simulation example is provided to illustrate the effectiveness of the proposed approach.

MSC:

93D15 Stabilization of systems by feedback
93C41 Control/observation systems with incomplete information
93C10 Nonlinear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Rui, C.; Reyhanoglu, M.; Kolmanovsky, I.; Cho, S.; McClamroch, N. H., Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system, Proceedings of the 36th IEEE Conference Decision Control
[2] Lin, W.; Qian, C., Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems, Systems & Control Letters, 39, 5, 339-351 (2000) · Zbl 0948.93056
[3] Qian, C.; Lin, W., A continuous feedback approach to global strong stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 46, 7, 1061-1079 (2001) · Zbl 1012.93053
[4] Lin, W.; Qian, C., Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework, IEEE Transactions on Automatic Control, 47, 5, 757-774 (2002) · Zbl 1364.93400
[5] Lin, W.; Qian, C., Adaptive control of nonlinearly parameterized systems: the smooth feedback case, IEEE Transactions on Automatic Control, 47, 8, 1249-1266 (2002) · Zbl 1364.93399
[6] Polendo, J.; Qian, C., A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback, International Journal of Robust and Nonlinear Control, 17, 7, 605-629 (2007) · Zbl 1113.93087
[7] Polendo, J.; Qian, C., An expanded method to robustly stabilize uncertain nonlinear systems, Communications in Information and Systems, 8, 1, 55-70 (2008) · Zbl 1158.93394
[8] Sun, Z.; Liu, Y., Adaptive stabilisation for a large class of high-order uncertain non-linear systems, International Journal of Control, 82, 7, 1275-1287 (2009) · Zbl 1168.93397
[9] Zhang, J.; Liu, Y., A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems, Science China: Information Sciences, 54, 7, 1419-1429 (2011) · Zbl 1267.93055
[10] Zhang, X.-H.; Xie, X.-J., Global state feedback stabilisation of nonlinear systems with high-order and low-order nonlinearities, International Journal of Control, 87, 3, 642-652 (2014) · Zbl 1317.93216
[11] Bhat, S. P.; Bernstein, D. S., Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization, 38, 3, 751-766 (2000) · Zbl 0945.34039
[12] Hong, Y.; Huang, J.; Xu, Y., On an output feedback finite-time stabilization problem, IEEE Transactions on Automatic Control, 46, 2, 305-309 (2001) · Zbl 0992.93075
[13] Hong, Y., Finite-time stabilization and stabilizability of a class of controllable systems, Systems & Control Letters, 46, 4, 231-236 (2002) · Zbl 0994.93049
[14] Huang, X.; Lin, W.; Yang, B., Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica, 41, 5, 881-888 (2005) · Zbl 1098.93032
[15] Hong, Y.; Wang, J.; Cheng, D., Adaptive finite-time control of nonlinear systems with parametric uncertainty, IEEE Transactions on Automatic Control, 51, 5, 858-862 (2006) · Zbl 1366.93290
[16] Hong, Y.; Jiang, Z.-P., Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties, IEEE Transactions on Automatic Control, 51, 12, 1950-1956 (2006) · Zbl 1366.93577
[17] Li, S.; Tian, Y.-P., Finite-time stability of cascaded time-varying systems, International Journal of Control, 80, 4, 646-657 (2007) · Zbl 1117.93004
[18] Nersesov, S. G.; Haddad, W. M.; Hui, Q., Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions, Journal of the Franklin Institute: Engineering and Applied Mathematics, 345, 7, 819-837 (2008) · Zbl 1169.93020
[19] Du, H.; Qian, C.; Frye, M. T.; Li, S., Global finite-time stabilisation using bounded feedback for a class of non-linear systems, IET Control Theory & Applications, 6, 14, 2326-2336 (2012)
[20] Ding, S.; Li, S.; Zheng, W. X., Nonsmooth stabilization of a class of nonlinear cascaded systems, Automatica, 48, 10, 2597-2606 (2012) · Zbl 1271.93116
[21] Shen, Y.; Huang, Y., Global finite-time stabilisation for a class of nonlinear systems, International Journal of Systems Science: Principles and Applications of Systems and Integration, 43, 1, 73-78 (2012) · Zbl 1259.93098
[22] Li, J.; Qian, C.; Ding, S., Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems, International Journal of Control, 83, 11, 2241-2252 (2010) · Zbl 1210.93064
[23] Yang, B.; Lin, W., Nonsmooth output feedback design with a dynamics gain for uncertain systems with strong nonlinearities, Proceedings of the 46th IEEE Conference Decision Control
[24] Khalil, H. K., Nonlinear Systems (2002), New Jersey, NJ, USA: Prentice-Hall, New Jersey, NJ, USA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.