×

Robust delayed-state-feedback stabilization of uncertain stochastic systems. (English) Zbl 1162.93389

Summary: Due to time spent in computation and transfer, control input is usually subject to delays. Problems of deterministic systems with input delay have received considerable attention. However, relatively few works are concerned with problems of stochastic system with input delay. This paper studies delayed-feedback stabilization of uncertain stochastic systems. Based on a new delay-dependent stability criterion established in this paper, a robust delayed-state-feedback controller that exponentially stabilizes the uncertain stochastic systems is proposed. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

MSC:

93D15 Stabilization of systems by feedback
93E03 Stochastic systems in control theory (general)
93E15 Stochastic stability in control theory
15A39 Linear inequalities of matrices
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Basin, M.V.; Rodkina, A.E., On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays, Nonlinear analysis. theory methods and applications, 68, 2147-2157, (2008) · Zbl 1154.34044
[2] Boyd, S.; EI Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control, (1994), SIAM Philadelphia
[3] Chen, W.-H.; Guan, Z.-H.; Lu, X., Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach, Systems & control letters, 54, 547-555, (2005) · Zbl 1129.93547
[4] Chen, W.-H.; Zheng, W.X., On improved robust stabilization of uncertain systems with unknown input delay, Automatica, 42, 1067-1072, (2006) · Zbl 1102.93033
[5] Feng, Z.; Liu, Y., Stability analysis and stabilization synthesis of stochastic large scale systems, (1995), Science Press Beijing
[6] Fridman, E., New Lyapunov-krasovskii functionals for stability of linear retarded and neutral type systems, Systems & control letters, 43, 309-319, (2001) · Zbl 0974.93028
[7] Fridman, E.; Shaked, U., An improved stabilization method for linear time-delay systems, IEEE transactions on automatic control, 47, 1931-1937, (2002) · Zbl 1364.93564
[8] Fridman, E.; Shaked, U., Delay-dependent stability and \(H_\infty\) control: constant and time-varying delays, International journal of control, 76, 48-60, (2003) · Zbl 1023.93032
[9] Gu, K. (2000). An integral inequality in the stability problem of time-delay systems. In Proceedings of the 39th IEEE conference on decision and control (pp. 2805-2810)
[10] Hale, J.K., Theory of functional differential equations, (1977), Springer-Verlag New York · Zbl 0425.34048
[11] He, Y.; Wang, Q.-G.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 371-376, (2007) · Zbl 1111.93073
[12] Huang, L.; Deng, F., Robust stability of perturbed large-scale multi-delay stochastic systems, Dynamics of continuous, discrete & impulsive systems. series B, 9, 525-537, (2002) · Zbl 1034.93065
[13] Huang, L., & Deng, F. (2007). Robust exponential stabilization of stochastic large-scale delay systems. In Proceedings of 2007 IEEE international conference on control and automation (pp. 107-112)
[14] Kim, D.S.; Lee, Y.S.; Kwon, W.H.; Park, P.G., Maximum allowable delay bounds of networked control systems, Control engineering practice, 11, 1301-1313, (2003)
[15] Kolmanovskii, V.B.; Myshkis, A., Introduction to the theory and applications of functional differential equations, (1999), Kluwer Academic Publishers Dordrecht · Zbl 0917.34001
[16] Lee, Y.S.; Moon, Y.S.; Kwon, W.H.; Park, P.G., Delay-dependent robust \(H_\infty\) control for uncertain systems with a state-delay, Automatica, 40, 65-72, (2004) · Zbl 1046.93015
[17] Li, H.; Chen, B.; Zhou, Q.; Lin, C., Delay-dependent robust stability for stochastic time-delay systems with polytopic uncertainties, International journal of robust and nonlinear control, 18, 1482-1492, (2008) · Zbl 1232.93092
[18] Liao, X.X.; Mao, X., Exponential stability of stochastic delay interval systems, Systems & control letters, 40, 171-181, (2000) · Zbl 0949.60068
[19] Luo, R.C.; Chung, L.-Y., Stabilization for linear uncertain system with time latency, IEEE transactions on industrial electronics, 49, 905-910, (2002)
[20] Mao, X., Robustness of exponential stability of stochastic differential delay equations, IEEE transactions on automatic control, 41, 442-447, (1996) · Zbl 0851.93074
[21] Mao, X., Razumikhin-type theorems on exponential stability of stochastic functional differential equations, Stochastic processes and their applications, 65, 233-250, (1996) · Zbl 0889.60062
[22] Mao, X.; Koroleva, N.; Rodkina, A., Robust stability of uncertain stochastic differential delay equations, Systems & control letters, 35, 325-336, (1998) · Zbl 0909.93054
[23] Mao, X., The Lasalle-type theorems for stochastic functional differential equations, Journal of mathematical analysis and applications, 7, 307-328, (2000) · Zbl 0993.60054
[24] Mao, X., Stochastic differential equations and applications, (2007), Horwood Publishing Chichester
[25] Moon, Y.S.; Park, P.G.; Kwon, W.H., Robust stabilization of uncertain input-delayed systems using reduction method, Automatica, 37, 307-312, (2001) · Zbl 0969.93035
[26] Moon, Y.S.; Park, P.G.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, International journal of control, 74, 1447-1455, (2001) · Zbl 1023.93055
[27] Park, P.G., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE transactions on automatic control, 44, 876-877, (1999) · Zbl 0957.34069
[28] Rodkina, A.E.; Basin, M.V., On delay-dependent stability for a class of nonlinear stochastic delay-differential equations, Mathematics of control, signals, and systems, 18, 187-197, (2006) · Zbl 1103.93043
[29] Shen, Y.; Luo, Q.; Mao, X., The improved Lasalle-type theorems for stochastic functional differential equations, Journal of mathematical analysis and applications, 318, 134-154, (2006) · Zbl 1090.60059
[30] Xu, B., Stability robustness bounds for linear systems with multiple time-varying delayed perturbations, International journal of systems science, 28, 1311-1317, (1997) · Zbl 0899.93029
[31] Xu, S.; Chen, T., Robust \(H_\infty\) control for uncertain stochastic systems with state delay, IEEE transactions on automatic control, 47, 2089-2094, (2002) · Zbl 1364.93755
[32] Xu., S.; Lam, J., Improved delay-dependent stability criteria for time-delay systems, IEEE transactions on automatic control, 50, 384-387, (2005) · Zbl 1365.93376
[33] Xu, S.; Shi, P.; Chu, Y.; Zou, Y., Robust stochastic stabilization and \(H_\infty\) control of uncertain neutral stochastic time-delay systems, Journal of mathematical analysis and applications, 314, 1-16, (2006) · Zbl 1127.93053
[34] Yue, D., Robust stabilization of uncertain systems with unknown input delay, Automatica, 40, 331-336, (2004) · Zbl 1034.93058
[35] Yue, D.; Han, Q.-L., Delay-dependent exponential stability of stochastic systems with time-varying delay nonlinearity, and Markovian switching, IEEE transactions on automatic control, 50, 217-222, (2005) · Zbl 1365.93377
[36] Yue, D.; Han, Q.-L., Delayed feedback control of uncertain systems with time-varying input delay, Automatica, 41, 233-240, (2005) · Zbl 1072.93023
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.