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Zha, Wenting; Zhai, Junyong; Fei, Shumin

Output feedback control for a class of stochastic high-order nonlinear systems with time-varying delays. (English) Zbl 1302.93236

Int. J. Robust Nonlinear Control 24, No. 16, 2243-2260 (2014).
Summary: This paper discusses the problem of output feedback stabilization for a more general class of stochastic high-order nonlinear systems with time-varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed-loop system is globally asymptotically stable in probability, by choosing an appropriate Lyapunov-Krasovskii functional. An example is given to illustrate the effectiveness of the proposed design procedure.

Cited in 22 Documents

MSC:

93E15 Stochastic stability in control theory
93B52 Feedback control
93E03 Stochastic systems in control theory (general)
93D15 Stabilization of systems by feedback

Keywords:

stochastic nonlinear systems; output feedback; time-varying delays; Lyapunov-Krasovskii functional
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\textit{W. Zha} et al., Int. J. Robust Nonlinear Control 24, No. 16, 2243--2260 (2014; Zbl 1302.93236)
Full Text: DOI

References:

[1] Qian, Non-lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization, Systems and Control Letters 42 (3) pp 185– (2001) · Zbl 0974.93050
[2] Polendo J Qian C A generalized framework for global output feedback stabilization of genuinely nonlinear systems Proceeding of the 44th IEEE Conference on Decision and Control 2005 2646 2651
[3] Ding, Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations, International Journal of Robust and Nonlinear Control 21 (3) pp 271– (2011) · Zbl 1213.93182
[4] Qian, Recursive observer design, homogeneous approximation, and nonsmooth output feedback stabilization of nonlinear systems, IEEE Transactions on Automatic Control 51 (9) pp 1457– (2006) · Zbl 1366.93523
[5] Zhai, Global practical tracking control for a class of uncertain nonlinear systems, IET Control Theory and Applications 5 (11) pp 1343– (2011)
[6] Florchinger, Lyapunov-like techniques for stochastic stability, SIAM Journal of Control and Optimization 33 (4) pp 1151– (1995) · Zbl 0845.93085
[7] Deng, Output-feedback stochastic nonlinear stabilization, IEEE Transactions on Automatic Control 44 (2) pp 328– (1999) · Zbl 0958.93095
[8] Deng, Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance, Systems and Control Letters 39 (3) pp 173– (2000) · Zbl 0948.93053
[9] Wu, Adaptive backstepping controller design using stochastic small-gain theorem, Automatica 43 (4) pp 608– (2007) · Zbl 1114.93104
[10] Liu, Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states, International Journal of Robust and Nonlinear Control 18 (6) pp 665– (2008) · Zbl 1284.93241
[11] Xie, Output-feedback control of a class of high-order stochastic nonlinear systems, International Journal of Control 82 (9) pp 1692– (2009) · Zbl 1190.93087
[12] Li, Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable, Automatica 46 (4) pp 752– (2010) · Zbl 1193.93146
[13] Gu, Stability of Time-Delay Systems (2003) · Zbl 1039.34067
[14] Hale, Introduction to Functional Differential Equations (1993) · Zbl 0787.34002
[15] Hua, Robust stabilization of a class of nonlinear time-delay systems, Applied Mathematics and Computation 155 (3) pp 737– (2004) · Zbl 1053.93037
[16] Jiao, Adaptive feedback control of nonlinear time-delay systems: The LaSalle-Razumikhin-based approach, IEEE Transactions on Automatic Control 50 (11) pp 1909– (2005) · Zbl 1365.93185
[17] Hua, Robust stabilization for a class of time-delay systems with triangular structure, IET Control Theory and Applications 1 (4) pp 875– (2007)
[18] Zhang, Adaptive stabilisation for a class of non-linear state time-varying delay systems with unknown time-delay bound, IET Control Theory and Applications 4 (10) pp 1905– (2009)
[19] Chen, State-feedback stabilization for a class of stochastic time-delay nonlinear systems, International Journal of Robust and Nonlinear Control 22 (17) pp 1921– (2012) · Zbl 1263.93184
[20] Liu, Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay, Automatica 47 (12) pp 2772– (2011) · Zbl 1235.93208
[21] Xie, A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay, IEEE Transactions on Automatic Control (2012)
[22] Xie, Further results on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay, Automatica 48 (10) pp 2577– (2012) · Zbl 1271.93122
[23] Krstić, Stabilization of Uncertain Nonlinear Systems (1998)
[24] Kawski M Stability and nilpotent approximations Proceeding of 27th IEEE Conference on Decision and Control 1988 1244 1248
[25] Liu, Adaptive output-feedback control for a class of uncertain stochastic nonlinear systems with time delays, International Journal of Control 81 (8) pp 1210– (2008) · Zbl 1152.93404
[26] Khalil, Nonlinear systems, 3. ed. (2002)
[27] Rosier, Homogeneous Lyapunov function for homogeneous continuous vector fields, Systems and Control Letters 19 (6) pp 467– (1992) · Zbl 0762.34032
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.