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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070275Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1226
 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.
 X. R. Mao, "Exponential stability of stochastic delay internal systems with Markovian switching". IEEE Trans. Autom. Control, vol. 47, pp. 1604-1612, 2002.
 X. R. Mao, C. G. Yuan, "Stochastic differential equaions with markovian switching," Imperial College Press, London, 2006.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 P. Park, J. W. Ko, "Stability and robust stability for systems with a time-varying delay," Automatica, vol. 43, pp. 1855-1858, 2007.
 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.
 E. Fridman, U. Shaked, K. Liu, "New conditions for delay-derivativedependent stability," Automatica, vol. 45, pp. 2723-2727, 2009.
 K. Q. Gu, V. Kharitonov, J. Chen, "Stability of time-delay systems", Boston: Birkhauser, 2003
 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.