Passive Control for Uncertain Stochastic Time-Delay Systems

Abstract:

This paper investigates the problems of delay-dependent passive analysis and control for uncertain stochastic systems with time-varying delay and norm-bounded parameters uncertainties. Delay-dependent stochastic passive condition for the uncertain stochastic time-delay systems is obtained based on Laypunov-Krasovkii functional approach. On the basis of this condition, a delay-dependent passive controller is presented. Sufficient condition for the existence of desired controller is formulated in terms of linear matrix inequality. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

• Periodical: Applied Mechanics and Materials (Volumes 58-60)
• Pages: 691-696
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.58-60.691
• Online since: June 2011
• Authors: Cheng Wang, Huan Bin Liu
• Keywords: Linear Matrix Inequality (LMI), Passivity, Time Delay, Uncertain Stochastic Systems

References

[1] S. Xu and T. Chen: Robust control for uncertain stochastic systems with state delay, IEEE Transactions on Automatic Control Vol. 47 (2002), p.2089-(2094).

DOI: 10.1109/tac.2002.805670

[2] J.W. Xia, S.Y. Xu and Y. Zhou: Robust control for stochastic uncertain systems with time-delay, Control Theory and Applications Vol. 25 (2008), pp.943-946.

[3] L.G. Wu, C.H. Wang and H.J. Gao: Stability of uncertain stochastic systems with time-varying delays based on parameter-dependent Laypunov functional, Control Theory and Applications Vol. 24 (2007), pp.607-612.

[4] D. Yue, Q.L. Han: Delay-dependent exponential stability of stochastic systems with time-varying delay nonlinearity and Markovian switching, IEEE Transactions on Automatic Control Vol. 50 (2005), pp.217-222.

DOI: 10.1109/tac.2004.841935

[5] H.Q. Lu and W.N. Zhou: Delay-dependent robust control for uncertain stochastic systems, Control and Decision Vol. 24 (2009), pp.76-80.

[6] S. Xu, P. Shi and Y. Chu: Robust stochastic stabilization and control of uncertain neutral stochastic time-delay systems, Journal of Mathematical Analysis and Application Vol. 314 (2006), pp.1-16.

DOI: 10.1016/j.jmaa.2005.03.088

[7] E. Fridman and U. Shaked: On delay-dependent passivity, IEEE Transactions Automatic Control, Vol. 47 (2002), pp.664-669.

DOI: 10.1109/9.995046

[8] B. Brogliato, R. Lozano and B. Maschke: Dissipative Systems Analysis and Control: Theory and Application (Springer-Verlag, London 2000).

[9] H.J. Gao, T.W. Chen and T.Y. Chai: Passivity and passification for networked control systems, SIAM Journal on control and Optimization Vol. 46 (2007), pp.1299-1322.

DOI: 10.1137/060655110

[10] W.H. Gui, B.Y. Liu and Z.H. Tang: A delay-dependent passivity criterion of linear neutral delay systems, Journal of Control Theory and Applications Vol. 4 (2006), pp.201-206.

DOI: 10.1007/s11768-006-4142-3

[11] W.H. Chen, Z.H. Guan and X.M. Lu: Passive control synthesis for uncertain Markovian jump systems with multiple mode-dependent time-delays, Asian Journal of Control Vol. 7 (2005), pp.135-143.

DOI: 10.1111/j.1934-6093.2005.tb00382.x

[12] S. He and F. Liu: Observer-based passive control for nonlinear uncertain time-delay jump systems, Acta Mathematica Scientia Vol. 29 (2009), pp.334-343.

[13] K.Q. Gu, V.L. Kharitonov and J. Chen: Stability of Time-delay System (Birkhauser, Boston 2003).