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A new approach to robust finite-time H∞ control of continuous-time Markov jump systems

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Języki publikacji
EN
Abstrakty
EN
This paper studies the robust finite-time H∞ state feedback control problem of continuous-time Markov jump systems (MJSs) subject to norm bounded uncertainties. Transition probabilities are allowed to be known, uncertain with known bounds or unknown. Based on the continuous transition probability property and the developed slack variable technique, Lyapunov variables are separatek from unknown transition probabilities and system matrices. With these separations, a relaxed method for robust finite-time H∞ controller design is proposed in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of and the benefit from the proposed method.
Rocznik
Strony
211--231
Opis fizyczny
Bibliogr. 34 poz., rys., tab.
Twórcy
autor
  • College of Electrical Engineering and Control Science, Nanjing Technology University, Nanjing, 211816, China
autor
  • Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing, 210096, China
  • College of Electrical Engineering and Control Science, Nanjing Technology University, Nanjing, 211816, China
autor
  • School of Automation, Southeast University, Nanjing, 210096, China
autor
  • College of Electrical Engineering and Control Science, Nanjing Technology University, Nanjing, 211816, China
Bibliografia
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  • 2. AMATO, F., ARIOLA, M. and COSENTINO, C. (2011) Robust finite-time stabilisation of uncertain linear systems. International Journal of Control, 84 (12), 2117-2127.
  • 3. AMATO, F., ARIOLA, M. and DORATE, P. (2001) Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica, 37 (9), 1459-1463.
  • 4. BOLZERN, P., COLANERI, P. and DE NICOLAO, G. (2013) Almost Sure Stability of Markov Jump Linear Systems With Deterministic Switching. IEEE Transactions on Automatic Control, 58 (1), 209-214. COSTA, O. L. V., FRAGOSO, M. D. and MARQUES, R. P. (2005) DiscreteTime Markov Jump Linear Systems. Probability and Its Applications series. Springer Verlag, New York.
  • 5. DE FARIAS, D. P., GEROMEL, J. C., DO VAL, J. B. and COSTA, O. L. V. (2000) Output feedback control of Markov jump linear systems in continuous-time. IEEE Transactions on Automatic Control, 45 (5), 944949.
  • 6. DONG, J., YANG, G. (2007) Fuzzy controller design for Markovian jump nonlinear systems. International Journal of Control, Automation, and Systems, 5 (6), 712-717.
  • 7. DONG, J., YANG, G. (2008) Robust H2 control of continuous-time Markov jump linear systems. Automatica, 44 (5), 1431-1436.
  • 8. 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 (1), 38-53.
  • 9. HE, S., LIU, F. (2010a) Robust peak to-peak filtering for Markov jump systems. Signal Processing, 90 (2), 513-522.
  • 10. HE, S., LIU, F. (2010b) Observer-based finite-time control of time-delayed jump systems. Applied Mathematics and Computation, 217 (6), 23272338. HE, S., LIU, F. (2012) Finite-time H∞ fuzzy control of nonlinear jump systems with time delays via dynamic observer-based dtate feedback. IEEE Transactions on Fuzzy Systems, 20 (4), 605-614.
  • 11. HUANG, J., SHI, Y. (2012) Stochastic stability and robust stabilization of semi-Markov jump linear systems. International Journal of Robust and Nonlinear Control, 23 (18), 2028-2043.
  • 12. JI, Y. and CHIZECK, H. J. (1990) Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control, 35 (7), 777-788.
  • 13. LUAN, X., LIU, F. and SHI, P. (2010) Finite-time filtering for non-linear stochastic systems with partially known transition jump rates. IET Control Theory & Applications, 4 (5), 735-745.
  • 14. LUAN, X., LIU, F. and SHI, P. (2011) Robust finite-time control for a class of extended stochastic switching systems. International Journal of Systems Science, 42 (7), 1197-1205.
  • 15. MA, S., BOUKAS, E. K. and CHINNIAH, Y. (2010) Stability and stabilization of discrete-time singular Markov jump systems with time-varying delay. International Journal of Robust and Nonlinear Control, 20 (5), 531-543.
  • 16. MARITON, M. (1990) Jump Linear Systems in Automatic Control. Marcel Dekker, New York.
  • 17. SHI, P., BOUKAS, E. K. and AGARWAL, R. K. (1999) Control of Markovian Jump Discrete-Time Systems with Norm Bounded Uncertainty and Unknown Delay. IEEE Transactions on Automatic Control, 44 (11), 21392144.
  • 18. SHEN, M., YANG, G. (2012a) New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities. IET Control Theory & Applications, 6 (14), 2318-2325.
  • 19. SHEN, M., YANG, G. (2012b) H2 filter design for discrete-time Markov jump linear systems with partly unknown transition probabilities. Optimal Control Applications and Methods, 33 (3), 318-337. SHEN, M., YE, D. (2013) Improved fuzzy control design for nonlinear Markovianjump systems with incomplete transition descriptions. Fuzzy Sets and Systems, 217 (16), 80-95.
  • 20. SUN, M., LAM, J., XU, S. and SHU, Z. (2012) Optimal time-weighted H2 model reduction for Markovian jump systems. International Journal of Control, 85 (6), 613-628.
  • 21. WANG, Y., XIE, L. and DE SOUZA, C. E. (1992) Robust control of a class of uncertain nonlinear systems. Systems and Control Letters, 19 (2), 139149.
  • 22. 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 Processing, 90 (2), 548-556.
  • 23. WU, Z., SHI, P., SU, H. and CHU, J. (2011) Passivity analysis for discretetime stochastic Markovian jump neural networks with mixed time-delays. IEEE Transactions on Neural Networks, 22 (10), 1566-1575.
  • 24. WU, Z., SHI, P., SU, H. and CHU, J. (2013) Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampleddata. IEEE Transactions on Cybernetics, 43 (6), 1796-1806.
  • 25. WU, Z., SHI, P., SU, H. and CHU, J. (2014) Asynchronous l2 −l∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica, 50 (1), 180-186. XIONG, J., LAM, J. (2005) On robust stabilisation of Markovian jump systems with uncertain switching probabilities. Automatica, 41(5), 897-903.
  • 26. YUE, D., HAN, Q. (2005) Delay-dependent exponential stability of stochastic systems with time varying delay, nonlinearity, and Markovian switching. IEEE Transactions on Automatic Control, 50 (2), 217-222. ZHANG, L., BOUKAS, E. K. (2009a) Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica, 45 (2), 463-468.
  • 27. ZHANG, L., BOUKAS, E. K. (2009b) Mode-dependent H∞ filtering for discretetime Markovian jump linear systems with partly unknown transition probabilities. Automatica , 45 (6), 1462-1467.
  • 28. ZHANG, L., BOUKAS, E. K. and LAM, J. (2008) Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Transactions on Automatic Control, 53 (10), 2458-2464.
  • 29. ZHANG, L., BOUKAS, E. K. and SHI, P. (2009) H∞ model reduction for discrete-time Markov jump linear systems with partially known transition probabilities. International Journal of Control, 82 (2), 343-351.
  • 30. ZHANG, L., CUI, N., LIU, M. and ZHAO, Ye. (2011) Asynchronous Filtering of Discrete-Time Switched Linear Systems with Average Dwell Time. IEEE Transactions on Circuits and Systems I, 58 (5), 1109 1118.
  • 31. ZHANG, L., GAO, H. and KAYNAK, O. (2013) Network-Induced Constraints in Networked Control Systems-A Survey. IEEE Transactions on Industrial Informatics, 9 (1), 403-416.
  • 32. ZHANG, L., ZHUANG, S. and SHI, P. (2015) Non-Weighted Quasi-TimeDependent H-infinity Filtering for Switched Linear Systems With Persistent Dwell-Time. Automatica, 54, 201-209.
  • 33. ZONG, G., YANG, D. (2014) Robust resilient H∞ control for stochastic systems with Markovian jump parameters under partially known transition probabilities. Optimal Control Applications and Methods, 35(5), 539-558.
  • 34. ZUO, Z., LI, H., LIU, Y. and WANG, Y. (2012) On finite-time stochastic stability and stabilization of Markovian jump systems subject to partial information on transition probabilities. Circuits Systems and Signal Processing, 31(6), 1973-1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-286d538e-f2b4-4616-a711-ac22fe287d80
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