H 2 state feedback controller design for continuous Markov jump linear systems with partly known information

International Journal of Systems Science

Volumn 43, Issue 4, 2012, Pages 786-796

  Shen, Mouquan ^a,b   Yang, Guang Hong ^a,b  

^a NORTHEASTERN UNIVERSITY   (China)

^b KEY LABORATORY OF INTEGRATED AUTOMATION OF PROCESS INDUSTRY   (China)

Author keywords

H 2 control; linear matrix inequality; partly known information; transition probability matrix

Indexed keywords

CONTROL PROBLEMS; LYAPUNOV MATRIX; MARKOV JUMP LINEAR SYSTEMS; NUMERICAL EXAMPLE; PARTLY KNOWN INFORMATION; PERFORMANCE ANALYSIS; STATE FEEDBACK CONTROLLER; SUFFICIENT CONDITIONS; TRANSITION PROBABILITIES; TRANSITION PROBABILITY MATRIX;

LINEAR MATRIX INEQUALITIES; STATE FEEDBACK;

PROBABILITY;

EID: 84857203210     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207721.2010.523799     Document Type: Article

References (27)

1. Bar-Shalom, Y., and Li, X.R. (1993), Estimation and Tracking: Principles, Techniques, and Software, Norwell, MA: Artech House.
2. Boukas, E.K. (2009), 'H∞ Control of Discrete-time Markov Jump Systems with Bounded Transition Probabilities', Optimal Control Application and Methods, 30, 477-494.
3. Boyd, S., Ghaoui, L.E., Feron, E., and Balakrishnan, V. (1994), Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA: SIAM.
4. 2 Control of Discrete-time Markovian Linear Systems', International Journal of Control, 66, 557-579. (Pubitemid 127549186)
5. de Farias, D.P., Geromel, J.C., do Val, J.B.R., and Costa, O.L.V. (2000), 'Output Feedback Control of Markov Jump Linear Systems in Continuous-time', IEEE Transactions on Automatic Control, 45, 944-949.
6. de Souza, C.E., Trofino, A., and Barbosa, K.A. (2006), 'Mode-independent H∞ Filter for Markovian Jump Linear Systems', IEEE Transactions on Automatic Control, 51, 1837-1841. (Pubitemid 44824371)
7. Dong, J., and Yang, G. (2008), 'Robust H∞ Control of Continuous-time Markov Jump Linear Systems', Automatica, 44, 1431-1436.
8. Fang, Y., and Loparo, K.A. (2002), 'Stabilization of Continuous-time Jump Linear Systems', IEEE Transactions on Automatic Control, 47, 1590-1603. (Pubitemid 35298546)
9. Feng, X., Loparo, K.A., Ji, Y., and Chizeck, H.J. (1992), 'Stochastic Stability Properties of Jump Linear Systems', IEEE Transactions on Automatic Control, 37, 38-53.
10. Fioravanti, A.R., Goncalves, A.P.C., and Geromel, J.C. (2008), 'H2 Filtering of Discrete-time Markov Jump Linear Systems Through Linear Matrix Inequalities', International Journal of Control, 81, 1221-1231.
11. Ghaoui, L.E., and Rami, M.A. (1996), 'Robust Statefeedback Stabilization of Jump Linear Systems via LMIs', International Journal on Robust Nonlinear Control, 6, 1015-1022.
12. Ji, Y., and Chizeck, H.J. (1990), 'Controllability, Stabilizability, and Continuous-time Markovian Jump Linear Quadratic Control', IEEE Transactions on Automatic Control, 35, 777-788. (Pubitemid 20726183)
13. Karan, M., Shi, P., and Kaya, C.Y. (2006), 'Transition Probability Bounds for the Stochastic Stability Robustness of Continuousand Discrete-time Markovian Jump Linear Systems', Automatica, 42, 2159-2168. (Pubitemid 44647194)
14. Li, L., Ugrinovskii, V.A., and Orsi, R. (2007), 'Decentralized Robust Control of Uncertain Markov Jump Parameter Systems via Output Feedback', Automatica, 43, 1932-1944. (Pubitemid 47576047)
15. Mariton, M. (1990), Jump Linear Systems in Automatic Control, New York: Marcel Dekker.
16. Shi, P., and Boukas, E.K. (1997), 'H∞ Control for Markovian Jumping Linear Systems with Parametric Uncertainty', Journal of Optimization Theory and Applications, 95, 75-99. (Pubitemid 127352340)
17. Shi, P., Boukas, E.K., and Agarwal, R.K. (1999), 'Kalman Filtering for Continuous-time Uncertain Systems with Markovian Jumping Parameters', IEEE Transactions on Automatic Control, 44, 1592-1597. (Pubitemid 30508570)
18. Sun, X., Liu, G., Reeds, D., and Wang, W. (2008), 'Stability of Systems with Controller Failure and Time-varying Delay', IEEE Transactions on Automatic Control, 53, 2391-2396.
19. Pakshin, P.V. (1997), 'Robust Stability and Stabilization of Family of Jumping Stochastic Systems', Nonlinear Analysis, 30, 2855-2866. (Pubitemid 127406953)
20. Wang, Z., Lam, J., and Liu, X. (2004), 'Exponential Filtering for Uncertain Markovian Jump Time-delay Systems with Nonlinear Disturbances', IEEE Transactions on Circuits and Systems II: Express Briefs, 51, 262-268.
21. Willsky, B.C., and Levy, A.S. (1979), 'Stochastic Stability Research for Complex Power Systems', Technical Report, Massachesetts Institute of Technology, Cambridge.
22. 2 Control of Markovian Jump Systems with Uncertain Switching Probabilities', International Journal of System Science, 40, 255-265.
23. Xiong, J., Lam, J., Gao, H., and Ho, D.W.C (2005), 'On Robust Stabilization of Markovian Jump Systems with Uncertain Switching Probabilities', Automatica, 41, 897-903. (Pubitemid 40352404)
24. Xu, S., Chen, T., and Lam, J. (2003), 'Robust H∞ Filtering for Uncertain Markovian Jump Systems with Mode-dependent Time-delays', IEEE Transactions on Automatic Control, 48, 900-907.
25. Xu, S., Chen, T., and Lam, J. (2004), 'Robust H∞ Filtering for a Class of Nonlinear Discrete-time Markovian Jump Systems', Journal of Optimization Theory and Applications, 122, 651-668. (Pubitemid 39332500)
26. Zhang, L., Boukas, E.K., and Lam, J. (2008), 'Analysis and Synthesis of Markov Jump Linear Systems with Time-varying Delays and Artially Known Transition Probabilities', IEEE Transactions on Automatic Control, 53, 2458-2464.
27. Zhang, L., Huang, B., and Lam, J. (2003), 'H∞ Model Reduction of Markovian Jump Linear Systems', Systems and Control Letters, 50, 103-118.