Delay-Dependent H∞ Performance Analysis for Markovian Jump Systems with Time-Varying Delays

This paper considers ­H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed ­H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.





References:
[1] C. G. Yuan, J. Lygeros, "Stabilization of a class of stochastic differential
equations with Markovian switching," Systems & Control Letters,
vol. 54, pp. 819-833, 2005.
[2] X. R. Mao, "Exponential stability of stochastic delay internal systems
with Markovian switching". IEEE Trans. Autom. Control, vol. 47, pp.
1604-1612, 2002.
[3] X. R. Mao, C. G. Yuan, "Stochastic differential equaions with markovian
switching," Imperial College Press, London, 2006.
[4] Y. He, Y. Zhang, M. Wu, J. H. She, "Improved exponential stability for
stochastic Markovian jump systems with nonlinearity and time-varying
delay," Int. J. Robust Nonlinear Control, vol. 20, pp. 16-26, 2010.
[5] S. Y. Xu, J. Lam, X. R. Mao, "Delay-Dependent ­ØÉ╗∞ Control and Filtering
for Uncertain Markovian Jump Systems With Time-Varying Delays,"
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, vol. 54, no. 9,
pp. 2070-2077, 2007.
[6] G. L. Wei, Z. D. Wang, H. S. Shu, "Nonlinear ­ØÉ╗∞ control of stochastic
time-delay systems with Markovian switching," Chaos, Solitons and
Fractals, vol. 35, pp. 442-451, 2008.
[7] Z. Y. Wang, L. H. Huang, X. X. Yang, "­ØÉ╗∞ performance for a
class of uncertain stochastic nonlinear Markovian jump systems with
time-varying delay via adaptive control method," Applied Mathematical
Modelling, vol. 35, pp. 1983-1993, 2011.
[8] H. Y. Li, B. Chen, Q. Zhou, C. Lin, "A Delay-Dependent Approach to
Robust ­ØÉ╗∞ Control for Uncertain Stochastic Systems with State and
Input Delays," Circuits Syst Signal Process, vol. 28, pp. 169-183, 2009.
[9] J. W. Xia, B. Song, J. W. Lu, "Robust ­ØÉ╗∞ Control for Stochastic
Time-Delay Systems with Markovian Jump Parameters via Parameter-
Dependent Lyapunov Functionals," Circuits Syst Signal Process, vol. 27,
pp. 331-349, 2008.
[10] G. L. Wang, Q. L. Zhang, V. Sreeram, "Robust delay-range-dependent
stabilization for Markovian jump systems with mode-dependent time
delays and nonlinearities," Optimal Control Applications and Methods,
vol. 31, no. 3, pp. 249-264, 2010.
[11] P. Park, J. W. Ko, "Stability and robust stability for systems with a
time-varying delay," Automatica, vol. 43, pp. 1855-1858, 2007.
[12] D. Yue, H. J. Li, "Synchronization stability of continuous/discrete
complex dynamical networks with interval time-varying delays," Neurocomputing,
vol. 73, pp. 809-819, 2010.
[13] E. Fridman, U. Shaked, K. Liu, "New conditions for delay-derivativedependent
stability," Automatica, vol. 45, pp. 2723-2727, 2009.
[14] K. Q. Gu, V. Kharitonov, J. Chen, "Stability of time-delay systems",
Boston: Birkhauser, 2003
[15] Z. G. Wu, H. Y. Su, J. Chu, "Delay-dependent ­ØÉ╗∞ filtering for
Markovian jump time-delay systems," Signal Process, vol. 90, pp. 1815-
1824, 2010.