0
Research Papers

Nonfragile H Filtering of Continuous Markov Jump Linear Systems With General Transition Probabilities

[+] Author and Article Information
Mouquan Shen

College of Automation and Electrical Engineering,
Nanjing University of Technology,
Nanjing 211816, China
e-mail: mouquanshen@gmail.com

Guang-Hong Yang

College of Information Science and Engineering,
State Key Laboratory of Synthetical Automation for Process Industries,
Northeastern University,
Shenyang 110819, China
e-mail: yangguanghong@ise.neu.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 8, 2012; final manuscript received January 9, 2013; published online February 21, 2013. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 135(3), 031005 (Feb 21, 2013) (8 pages) Paper No: DS-12-1254; doi: 10.1115/1.4023403 History: Received August 08, 2012; Revised January 09, 2013

This paper concerns the mode dependent H filter design for continuous Markov jump linear systems. The filter gain to be designed is assumed to have additive variations and the transition probabilities are allowed to be known, uncertain with known bounds and unknown. Attention is focused on the design of a mode dependent nonfragile full order filter, which guarantees the filtering error system to be stochastically stable and has a prescribed H disturbance attenuation performance. Sufficient conditions for the desired filter design are given in the framework of linear matrix inequality. If the filter gain variations become zero and the transition probabilities are completely known, the proposed method is reduced to the standard H filtering results. A numerical examples is given to show the effectiveness of the proposed method.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Boukas, E. K., 2005, Stochastic Switching Systems: Analysis and Design, Birkhauser, Berlin.
Costa, O. L. V., Fragoso, M. D., and Marques, R. P., 2005, Discrete-Time Markov Jump Linear Systems, Springer-Verlag, London.
Mariton, M., 1990, Jump Linear Systems in Automatic Control, Marcel Dekker, New York.
Feng, X., Loparo, K. A., Ji, Y., and Chizeck, H. J., 1992, “Stochastic Stability Properties of Jump Linear Systems,” IEEE Trans. Autom. Control, 37(1), pp. 38–53. [CrossRef]
Boukas, E. K., 2009, “H Control of Discrete-Time Markov Jump Systems With Bounded Transition Probabilities,” Opt. Control Appl. Methods, 30(5), pp. 477–494. [CrossRef]
Zhang, L., and Lam, J., 2010, “Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions,” IEEE Trans. Autom. Control, 53(10), pp. 1695–1701. [CrossRef]
Liu, H., Ho, D.W.C., and Sun, F., 2008, “Design of H Filter for Markov Jumping Linear Systems With Non-Accessible Mode Information,” Automatica, 44(10), pp. 2655–2660. [CrossRef]
Ji, Y., and Chizeck, H., 1990, “Controllability, Stabilizability, and Continuous Time Markovian Jump Linear Quadratic Control,” IEEE Trans. Autom. Control, 35(7), pp. 777–788. [CrossRef]
Costa, O. L. V., and Guerra, S., 2002, “Robust Linear Filtering for Discrete-Time Hybrid Markov Linear Systems,” Int. J. Control, 75(10), pp. 712–727. [CrossRef]
Xiong, J., and Lam, J., 2006, “Fixed-Order Robust H Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities,” IEEE Trans. Signal Process., 54(4), pp. 1421–1430. [CrossRef]
Zhang, H., Shi, Y., and Mehr, A. S., 2011, “Robust Weighted H Filtering for Networked Systems With Intermittent Measurements of Multiple Sensors,” Int. J. Adapt. Control Signal Process, 25(4), pp. 313–330. [CrossRef]
Zhang, H., Shi, Y., and Mehr, A. S., 2010, “Robust Energy-to-Peak Filtering for Networked Systems With Time-Varying Delays and Randomly Missing Data,” IET Control Theory & Applications, 4(12), pp. 2921–2936. [CrossRef]
Ding, D., and Yang, G., 2010, “Fuzzy Filter Design for Nonlinear Systems in Finite-Frequency Domain,” IEEE Trans. Fuzzy Syst., 18(5), pp. 935–945. [CrossRef]
Zhang, H., Shi, Y., Mehr, A. S., and Huang, H., 2011, “Robust Energy-to-Peak FIR Equalization for Time-Varying Communication Channels With Intermittent Observations,” Signal Process., 91(7), pp. 1651–1658. [CrossRef]
Zhang, H., Shi, Y., and Mehr, A. S., 2012, “On H Filtering for Discrete-Time Takagi-Sugeno Fuzzy Systems,” IEEE Trans. Fuzzy Syst., 20(2), pp. 396–401. [CrossRef]
Wang, G., Zhang, Q., and Sreeram, V., 2009, “Design of Reduced-Order H Filtering for Markovian Jump Systems With Mode-Dependent Time Delays,” Signal Process., 89(2), pp. 187–196. [CrossRef]
Wang, G., Zhang, Q., and Sreeram, V., 2010, “Partially Mode-Dependent H Filtering for Discrete-Time Markovian Jump Systems With Partly Unknown Transition Probabilities,” Signal Process., 90(2), pp. 548–556. [CrossRef]
Han, C., and Zhang, H., 2009, “Linear Optimal Filtering for Discrete-Time Systems With Random Jump Delays,” Signal Process., 89(6), pp. 1121–1128. [CrossRef]
Zhang, H., Mehr, A. S., and Shi, Y., 2010, “Improved Robust Energy-to-Peak Filtering for Uncertain Linear Systems,” Signal Process., 90(9), pp. 2667–2675. [CrossRef]
De Souza, C. E., and Fragoso, M. D., 2002, “H Filtering for Markovian Jump Linear Systems,” Int. J. Syst. Sci., 33(11), pp. 909–915. [CrossRef]
Li, H., and Fu, M., 1997, “A Linear Matrix Inequality Approach to Robust H Filtering,” IEEE Trans. Signal Process., 45(9), pp. 2338–2350. [CrossRef]
Shi, P., Boukas, E. K., and Agarwal, R. K., 1999, “Kalman Filtering for Continuous-Time Uncertain Systems With Markovian Jumping Parameters,” IEEE Trans. Autom. Control, 44(8), pp. 1592–1597. [CrossRef]
Yaz, E. E., and Yaz, Y. I., 2000, “Reduced-Order Filtering of Jump Markov Systems With Noise-Free Measurements,” J. Franklin Inst., 337(7), pp. 923–928. [CrossRef]
Wang, Z., Lam, J., and Liu, X., 2003, “Nonlinear Filtering for State Delayed Systems With Markovian Switching,” IEEE Trans. Signal Process., 51(9), pp. 2321–2328. [CrossRef]
Wang, Z., Lam, J., and Liu, X., 2004, “Exponential Filtering for Uncertain Markovian Jump Time-Delay Systems With Nonlinear Disturbances,” IEEE Trans. Circuits Syst., II: Express Briefs, 51(5), pp. 262–268. [CrossRef]
Fang, Y., and Loparo, K. A., 2002, “Stabilization of Continuous-Time Jump Linear Systems,” IEEE Trans. Autom. Control, 47(10), pp. 1590–1603. [CrossRef]
Sworder, D. D., 1969, “Feedback Control for a Class of Linear Systems With Jump Parameters,” IEEE Trans. Autom. Control, 14(1), pp. 9–14. [CrossRef]
Costa, O. L. V., 1994, “Linear Minimum Mean Squares Error Estimation for Discrete-Time Markovian Jump Linear Systems,” IEEE Trans. Autom. Control, 39(8), pp. 1685–1689. [CrossRef]
Blom, H. A. P., and Bar-Shalom, Y., 1988, “The Interacting Multiple Model Algorithm for Systems With Markovian Switching Coefficients,” IEEE Trans. Autom. Control, 33(8), pp. 780–783. [CrossRef]
deSouza, C. E., and Fragoso, M. D., 2002, “Robust H Filtering for Uncertain Markovian Jump Linear Systems,” Int. J. Robust Nonlinear Control, 12(5), pp. 435–446. [CrossRef]
Xu, S., Chen, T., and Lam, J., 2003, “Robust H Filtering for Uncertain Markovian Jump Systems With Mode-Dependent Time Delays,” IEEE Trans. Autom. Control, 48(5), pp. 900–907. [CrossRef]
de Souza, C. E., Trofino, A., and Barbosa, K. A., 2006, “Mode-Independent H Filters for Markovian Jump Linear Systems,” IEEE Trans. Autom. Control, 51(11), pp. 1837–1841. [CrossRef]
Chang, X., and Yang, G., 2011, “Nonfragile H Filtering of Continuous-Time Fuzzy Systems,” IEEE Trans. Signal Process., 59(4), pp. 1528–1538. [CrossRef]
Keel, L. H., and Bhattacharyya, S. P., 1997, “Robust, Fragile, or Optimal?,” IEEE Trans. Autom. Control, 42(8), pp. 1098–1105. [CrossRef]
Yang, G., and Che, W., 2008, “Non-Fragile H Filter Design for Linear Continuous-Time Systems,” Automatica, 44(11), pp. 2849–2856. [CrossRef]
Ding, D., Li, X., Yin, Y., and Sun, C., 2012, “Nonfragile H and H2 Filter Designs for Continuous-Time Linear Systems Based on Randomized Algorithms,” IEEE Trans. Ind. Electron. Control Instrum., 59(11), pp. 4433–4442. [CrossRef]
Kang, Y., Zhang, J., and Ge, S. S., 2008, “Robust Output Feedback H Control of Uncertain Markovian Jump Systems With Mode-Dependent Time-Delays,” Int. J. Control, 81(1), pp. 43–61. [CrossRef]
Li, H., and Shi, Y., 2012, “ Robust H Filtering for Nonlinear Stochastic Systems With Uncertainties and Random Delays Modeled by Markov Chains,” Automatica, 48(1), pp. 159–166. [CrossRef]
Shen, M., and Yang, G., 2012, “H2 Filter Design for Discrete Markov Jump Linear System With Partly Unknown Transition Probabilities,” Opt. Control Appl. Methods, 33(3), pp. 318–337. [CrossRef]
Cao, Y., and Frank, M., 2000, “Robust H Disturbance Attenuation for a Class of Uncertain Discrete-Time Fuzzy Systems,” IEEE Trans. Fuzzy Syst., 8(4), pp. 406–415. [CrossRef]
Duan, Z., Zhang, J., Zhang, C., and Mosca, E., 2006, “Robust H2 and H Filtering for Uncertain Linear Systems,” Automatica, 42(11), pp. 1919–1926. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

One possible system mode

Grahic Jump Location
Fig. 2

Estimation error e(t) curves for partly known with nonfragile (solid) and without nonfragile (dashed)

Grahic Jump Location
Fig. 3

Estimation error e(t) curves for completely known with nonfragile (solid) and without nonfragile (dashed)

Grahic Jump Location
Fig. 4

Estimation error e(t) curves for completely known (solid) and partly known with nonfragile (dashed)

Grahic Jump Location
Fig. 5

Estimation error e(t) curves for completely known (solid) and partly known without nonfragile (dashed)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In