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Research Papers

H State-Feedback Control for Semi-Markov Jump Linear Systems With Time-Varying Delays

[+] Author and Article Information
Ji Huang

e-mail: jihuang@uvic.ca

Yang Shi

e-mail: yshi@uvic.ca
Department of Mechanical Engineering,
University of Victoria,
P.O. Box 3055, STN CSC,
Victoria, BC, V8W 3P6, Canada

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received February 2, 2012; final manuscript received March 1, 2013; published online May 21, 2013. Assoc. Editor: Eugenio Schuster.

J. Dyn. Sys., Meas., Control 135(4), 041012 (May 21, 2013) (8 pages) Paper No: DS-12-1044; doi: 10.1115/1.4024009 History: Received February 02, 2012; Revised March 01, 2013

Semi-Markov jump linear systems (S-MJLSs) are more general than Markov jump linear systems in modeling practical systems. This paper investigates the H control problem for a class of semi-Markov jump linear systems with time-varying delays. The sojourn-time partition technique is firstly proposed for the delayed stochastic switching system. A sufficient condition for designing the state feedback controller is then established. Moreover, the sufficient condition is expressed as a set of linear matrix inequalities which can be readily solved. A numerical example illustrates the effectiveness of the proposed controller design technique.

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References

Boukas, E. K., and Liu, Z. K., 2003, “Robust Stability and H Control of Discrete-Time Jump Linear Systems With Time-Delay: An LMI Approach,” ASME J. Dyn. Sys., Meas. Control, 125(2), pp. 271–277. [CrossRef]
Wen, J., and Liu, F., 2011, “Receding Horizon Control for Constrained Markovian Jump Linear Systems With Bounded Disturbance,” ASME J. Dyn. Sys., Meas. Control, 133(1), p. 011005. [CrossRef]
Shi, Y., and Yu, B., 2011, “Robust Mixed H2/H Control of Networked Control Systems With Random Time Delays in Both Forward and Backward Communication Links,” Automatica, 47(4), pp. 754–760. [CrossRef]
Shi, Y., and Yu, B., 2009, “Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains,” IEEE Trans. Autom. Control, 54(7), pp. 1668–1674. [CrossRef]
Wu, N. E., 2004, “Coverage in Fault-Tolerant Control,” Automatica, 40(4), pp. 537–548. [CrossRef]
Mariton, M., 1990, Jump Linear Systems in Automatic Control, M. Dekker, New York.
Schwartz, C., 2003, “Control of Semi-Markov Jump Linear Systems With Application to the Bunch-Train Cavity Interaction,” Ph.D. thesis, Northwestern University, Evanston, IL.
Schwartz, C., and Haddad, A., 2003, “Control of Jump Linear Systems Having Semi-Markov Sojourn Times,” Proceedings of the IEEE Conference on Decision and Control, Vol. 3, pp. 2804–2805. [CrossRef]
Huang, J., and Shi, Y., 2011, “Stochastic Stability of Semi-Markov Jump Linear Systems: An LMI Approach,” Proceedings of the IEEE Conference on Decision and Control, pp. 4668–4673. [CrossRef]
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory, Vol. 15, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Zhou, K., and Doyle, J., 1998, Essentials of Robust Control, Vol. 104, Prentice Hall, Englewood Cliffs, NJ.
Gahinet, P., Nemirovskii, A., Laub, A., and Chilali, M., 1994, “The LMI Control Toolbox,” Proceedings of the IEEE Conference on Decision and Control, Vol. 3, pp. 2038–2041. [CrossRef]
Chen, W.-H., Guan, Z.-H., and Yu, P., 2004, “Delay-Dependent Stability and H Control of Uncertain Discrete-Time Markovian Jump Systems With Mode-Dependent Time Delays,” Syst. Control Lett., 52(5), pp. 361–376. [CrossRef]
Boukas, E., and Liu, Z., 2001, “Robust H Control of Discrete-Time Markovian Jump Linear Systems With Mode-Dependent Time-Delays,” IEEE Trans. Autom. Control, 46(12), pp. 1918–1924. [CrossRef]
Gao, J., Huang, B., and Wang, Z., 2001, “LMI-Based Robust H Control of Uncertain Linear Jump Systems With Time-Delays,” Automatica, 37(7), pp. 1141–1146. [CrossRef]
Mirkin, B. M., and Gutman, P.-O., 2003, “Output-Feedback Model Reference Adaptive Control for Continuous State Delay Systems,” ASME J. Dyn. Sys., Meas., Control, 125(2), pp. 257–261. [CrossRef]
Wang, D.-J., 2004, “A New Approach to Delay-Dependent H Control of Linear State-Delayed Systems,” ASME J. Dyn. Sys., Meas., Control, 126(1), pp. 201–205. [CrossRef]
Li, H., and Shi, Y., 2012, “Robust H Filtering for Nonlinear Stochastic Systems With Uncertainties and Markov Delays,” Automatica, 48(1), pp. 159–166. [CrossRef]
Wang, Q., Lam, J., Xu, S., and Zhang, L., 2006, “Delay-Dependent γ-Suboptimal H Model Reduction for Neutral Systems With Time-Varying Delays,” ASME J. Dyn. Sys., Meas., Control, 128(2), pp. 394–399. [CrossRef]
Gao, H., Chen, T., and Lam, J., 2008, “A New Delay System Approach to Network-Based Control,” Automatica, 44(1), pp. 39–52. [CrossRef]
Zhang, L., Boukas, E., and Lam, J., 2008, “Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities,” IEEE Trans. Autom. Control, 53(10), pp. 2458–2464. [CrossRef]
Muliere, P., Secchi, P., and Walker, S. G., 2003, “Reinforced Random Processes in Continuous Time,” Stochastic Proc. Appl., 104(1), pp. 117–130. [CrossRef]
Boukas, E., 2006, Stochastic Switching Systems: Analysis and Design, Birkhauser, Boston, MA.
Svishchuk, A., 2000, Random Evolutions and Their Applications: New Trends, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Amri, I., Soudani, D., and Benrejeb, M., 2011, “Robust State-Derivative Feedback LMI-Based Designs for Time-Varying Delay System,” Proceedings of the 2011 International Conference on Communications, Computing and Control Applications (CCCA), pp. 1–6. [CrossRef]
Luan, X., Liu, F., and Shi, P., 2011, “Finite-Time Stabilization of Stochastic Systems With Partially Known Transition Probabilities,” ASME J. Dyn. Sys., Meas., Control, 133(1), p. 014504. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The relation of jump linear systems, S-MJLSs, and MJLSs

Grahic Jump Location
Fig. 2

The state trajectories of the closed-loop S-MJLS using the proposed controller in Eq. (25)

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