×

Output feedback control for stochastic nonlinear time delay systems using dynamic gain technique. (English) Zbl 1393.93115

Summary: This paper investigates the output feedback control for a class of stochastic nonlinear time delay systems based on dynamic gain technique. The nonlinear terms of the stochastic system satisfy linear growth condition on unmeasured state variables with the output dependent incremental rate, which makes the studied time delay stochastic system more general than the exiting results. Firstly, the full order dynamic gain observer is constructed. Then, a linear-like controller is designed without using recursive design method. Next, the stability analysis is given and a useful corollary is obtained. Finally, a simulation is given to illustrate the effectiveness of the proposed method.

MSC:

93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
93B52 Feedback control
93E15 Stochastic stability in control theory
Full Text: DOI

References:

[1] K. Gu, V. L. Kharitonov, J. Chen, Stability of time-delay systems, Birkhäuser, Berlin, Germany, 2003.; K. Gu, V. L. Kharitonov, J. Chen, Stability of time-delay systems, Birkhäuser, Berlin, Germany, 2003. · Zbl 1039.34067
[2] Lin, C.; Wang, Q.; Lee, T.; He, Y., LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems with Time Delay, (2007), SpringerVerlag New York · Zbl 1119.93002
[3] Hua, C.; Feng, G.; Guan, X., Robust controller design of a class of nonlinear time delay systems via backstepping method, Automatica, 44, 567-573, (2008) · Zbl 1283.93099
[4] Zhang, X.; Lin, Y., Adaptive control of nonlinear time-delay systems with application to a two-stage chemical reactor, IEEE Trans. Autom. Control, 60, 4, 1074-1079, (2015) · Zbl 1360.93370
[5] Hua, C.; Guan, X., Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks, IEEE Trans. Neural Netw., 19, 4, 673-688, (2008)
[6] Mahmoud, M. S.; Baig, M. H., Networked feedback control for nonlinear systems with random varying delays, J. Frankl. Inst., 351, 6, 3145-3162, (2014) · Zbl 1290.93072
[7] Mao, X., Exponential Stability of Stochastic Differential Equations, (1994), Dekker New York · Zbl 0806.60044
[8] Mao, X., A note on the Lasalle-type theorems for stochastic differential delay equations, J. Math. Anal. Appl., 268, 125-142, (2002) · Zbl 0996.60064
[9] Mao, X., Stochastic Differential Equation and Applications, (2007), Horwood Publishing · Zbl 1138.60005
[10] Xie, X.; Liu, L., A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay, IEEE Trans. Autom. Control, 58, 2, 494-499, (2013) · Zbl 1369.93513
[11] Liu, S.; Ge, S.; Zhang, J., Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays, Int. J. Control,, 81, 8, 1210-1220, (2008) · Zbl 1152.93404
[12] Fu, Y.; Tian, Z.; Shi, S., Output feedback stabilization for a class of stochastic time-delay nonlinear systems, IEEE Trans. Autom. Control, 50, 6, 847-851, (2005) · Zbl 1365.93395
[13] Jiao, T.; Xu, S.; Lu, J.; Wei, Y.; Zou, Y., Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via Lasalle-yoshizawa-type theorem, Int. J. Control, 89, 1, 69-83, (2016) · Zbl 1332.93362
[14] Jiang, M.; Zhang, K.; Xie, X., Output feedback stabilisation of stochastic nonlinear time-delay systems with unknown output function, Int. J. Syst. Sci., 48, 11, 2262-2271, (2017) · Zbl 1372.93159
[15] Liu, L.; Yin, S.; Zhang, L.; Yin, X.; Yan, H., Improved results on asymptotic stabilization for stochastic nonlinear time-delay systems with application to a chemical reactor system, IEEE Trans. Syst. Man Cybernet. Syst., 47, 1, 195-204, (2017)
[16] Cui, P.; Zhang, C.; Zhang, X., Global stabilization of uncertain stochastic nonlinear time-delay systems by output feedback, Int. J. Robust Nonlinear Control, (2007)
[17] Liu, L.; Xie, X., Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay, Automatica, 47, 2772-2779, (2011) · Zbl 1235.93208
[18] Xie, X.; Liu, L., Further results on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay, Automatica, 48, 2577-2586, (2012) · Zbl 1271.93122
[19] Xue, L.; Zhang, W.; Lin, Y., Global output tracking control for high-order stochastic nonlinear systems with SISS inverse dynamics and time-varying delays, J. Frankl. Inst., 353, 3249-3270, (2016) · Zbl 1344.93092
[20] Miao, X.; Li, L., Adaptive observer-based control for uncertain nonlinear stochastic systems with time-delay, J. Frankl. Inst., 353, 3595-3609, (2016) · Zbl 1347.93251
[21] Liu, L.; Xie, X., State feedback stabilization for stochastic feedforward non-linear systems with time-varying delay, Automatica, 94, 4, 936-942, (2013) · Zbl 1284.93187
[22] Praly, L.; Jiang, Z. P., Linear output feedback with dynamic high gain for nonlinear systems, Syst. Control Lett., 53, 107-116, (2004) · Zbl 1157.93494
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.