A New Controller of Stochastic Delay Systems

Abstract:

By introducing an additional vector, a new delay-dependent controller is designed for stochastic systems with time delay in this paper. The presented controller is formulated by means of LMI, and it guarantees robust asymptotical mean-square stability of the resulting closed-loop system. Our result shows advantage over some existing ones, which is demonstrated by a numerical example.

• Periodical: Applied Mechanics and Materials (Volumes 63-64)
• Pages: 974-977
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.63-64.974
• Online since: June 2011
• Authors: Yun Chen, Qing Qing Li
• Keywords: Additional Vector, Control, Stochastic Delay Systems

References

[1] C. -Y. Lu, S. -H. Tsai, G. -J. Jong and T.J. Su: An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays. IEEE Trans. Automatic Control, Vol. 48(2003), p.286.

DOI: 10.1109/tac.2002.808482

[2] H. Gao, C. Wang, and L. Zhao: Comments on An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays,. IEEE Trans. Automatic Control, 48(2003), p. (2073).

DOI: 10.1109/tac.2003.819305

[3] C. -Y. Lu, T.J. Su and S. -H. Tsai: On robust stabilization of uncertain stochastic time-delay systems-an LMI-based approach, Journal of the Franklin Institute, Vol. 342 (2005), p.473.

DOI: 10.1016/j.jfranklin.2005.01.004

[4] S. Xu, P. Shi, Y. Chu and Y. Zou: Robust stochastic stabilization and H∞ control of uncertain neutral stochastic time-delay systems, Journal of Mathematical Analysis and Applications, Vol. 314 (2006), p.1.

DOI: 10.1016/j.jmaa.2005.03.088

[5] A. -M. Stoica, I. Yaesh: Markovian jump delayed Hopfield networks with multiplicative noise. Automatica, Vol. 44 (2008), p.2157.

DOI: 10.1016/j.automatica.2007.12.013

[6] Y. Chen, A. Xue, S. Zhou, and R. Lu: Delay-dependent robust control for uncertain stochastic time-delay systems. Circuits, Systems, and Signal Processing, Vol. 27 (2008), p.447.

DOI: 10.1007/s00034-008-9037-8

[7] Y. Chen, H. Wang, A. Xue and R. Lu: Passivity analysis of stochastic time-delay neural networks. Nonlinear Dynamics, Vol. 61 (2010), p.71.

DOI: 10.1007/s11071-009-9632-7

[8] K. Gu, V.L. Kharitonov and J. Chen: Stability of Time-Delay Systems (Springer, Berlin, 2003).

[9] Q. -L. Han: On designing time-varying delay feedback controllers for master-slave synchronization of Lur'e systems. IEEE Trans. Circuits Syst. I, Regular Papers, Vol. 54 (2007), p.1573.

DOI: 10.1109/tcsi.2007.899627

[10] B. Øksendal: Stochastic Differential Equations: An Introduction with Applications (Springer, New York, 2003).