Robust finite-time H infin control for uncertain discrete jump systems with time delay

Applied Mathematics and Computation

Volumn 219, Issue 5, 2012, Pages 2465-2477

  Zhang, Yingqi ^a   Liu, Caixia ^a   Sun, Huixia ^a  

^a HENAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Discrete time systems; Linear matrix inequalities (LMIs); Markovian jump systems; Stochastic finite time boundedness; Time delay systems

Indexed keywords

DISCRETE TIME SYSTEM; FINITE TIME BOUNDEDNESS (FTB); LINEAR MATRIX INEQUALITY (LMIS); MARKOVIAN JUMP SYSTEMS; TIME-DELAY SYSTEMS;

DELAY CONTROL SYSTEMS; DIGITAL CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; MARKOV PROCESSES; STABILIZATION; STOCHASTIC SYSTEMS; TIME DELAY;

DISCRETE TIME CONTROL SYSTEMS;

EID: 84868204257     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.08.082     Document Type: Article

References (56)

1. N.N. Krassovskii, and E.A. Lidskii Analytical design of controllers in systems with random attributes Automat. Rem. Control 22 1961 1021 1025 1141-1146, 1289-1294
2. O.L.V. Costa, and M.D. Fragoso Stability results for discrete-time linear systems with Markovian jumping parameters J. Math. Anal. Appl. 179 1 1993 154 178
3. X. Mao Stability of stochastic differential equations with Markovian switching Stoch. Process. Appl. 79 1 1999 45 67 (Pubitemid 129570208)
4. H.J. Chizeck, A.S. Willsky, and D. Castanon Discrete-time Markovian jump linear quadratic optimal control Int. J. Control 43 1 1986 213 231 (Pubitemid 16472738)
5. O.L.V. Costa, and W.L. de Paulo Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems Automatica 43 4 2007 587 597 (Pubitemid 46341250)
6. C.E. Souza Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems IEEE Trans. Automat. Control 51 5 2006 836 841 (Pubitemid 43792649)
7. M. Karan, P. Shi, and C.Y. Kaya Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems Automatica 42 12 2006 2159 2168 (Pubitemid 44647194)
8. infin control of discrete-time Markovian jump linear systems IEEE Trans. Automat. Control 43 1 1998 95 100 (Pubitemid 128743108)
9. infin control for discrete-time jump linear systems with time delay J. Franklin Inst. 336 8 1999 1263 1281 (Pubitemid 30576858)
10. P. Shi, E.K. Boukas, and R.K. Agarwal Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay IEEE Trans. Automat. Control 44 11 1999 2139 2144 (Pubitemid 30531659)
11. infin control for uncertain discrete stochastic time-delay systems Syst. Control Lett. 51 3-4 2004 203 215
12. infin performance for a class of uncertain stochastic nonlinear Markovian jump systems with time-varying delay via adaptive control method Appl. Math. Model. 35 4 2011 1983 1993
13. infin filtering for uncertain Markovian jump systems with mode-dependent time delays IEEE Trans. Automat. Control 48 5 2003 900 907
14. M.S. Mahmoud, P. Shi, and A. Ismail Robust Kalman filtering for discrete-time Markovian jump systems with parameter uncertainty J. Comput. Appl. Math. 169 1 2004 53 69 (Pubitemid 38804604)
15. infin filtering for polytopic discrete-time systems IEEE Trans. Signal Process. 53 8 2005 3183 3191
16. infin filtering for Markovian jump systems with time-varying delays Int. J. Innovative Comput. Inform. Control 7 3 2011 1299 1310
17. E.K. Boukas, and P. Shi Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters Int. J. Robust Nonlinear Control 8 13 1998 1155 1167 (Pubitemid 128632068)
18. P. Shi, Y. Xia, G. Liu, and D. Rees On designing of sliding mode control for stochastic jump systems IEEE Trans. Automat. Control 51 1 2006 97 103 (Pubitemid 43137935)
19. L. Wu, P. Shi, and H. Gao State estimation and sliding mode control of Markovian jump singular systems IEEE Trans. Automat. Control 55 5 2010 1213 1219
20. Y. Yin, P. Shi, and F. Liu Gain scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities J. Franklin Inst. 348 4 2011 685 702
21. H.J. Kushner Stochastic Stability and Control 1967 Academic Press New York
22. O.L.V. Costa, M.D. Fragoso, and R.P. Marques Discrete-Time Markov Jump Linear Systems 2005 Springer London
23. F. Amato, M. Ariola, and P. Dorato Finite-time control of linear systems subject to parametric uncertainties and disturbances Automatica 37 9 2001 1459 1463 (Pubitemid 32691042)
24. A. EI-Gohary Optimal control of an angular motion of a rigid body during infinite and finite-time intervals Appl. Math. Comput. 141 2-3 2003 541 551
25. A. EI-Gohary, and A.S. AI-Ruzaiza Optimal control of non-homogenous prey-predator models during infinite and finite-time intervals Appl. Math. Comput. 146 2-3 2003 495 508
26. P. Dorato, Short time stability in linear time-varying systems, in: Proceedings of IRE International Convention Record, Part 4, New York, USA, 1961, pp. 83-87.
27. L. Weiss, and E.F. Infante Finite time stability under perturbing forces and on product spaces IEEE Trans. Automat. Control 12 1 1967 54 59
28. H. D'Angelo Linear Time-Varying Systems: Analysis and Synthesis 1970 Allyn and Bacon Boston
29. H.J. Kushner Finite-time stochastic stability and the analysis of tracking systems IEEE Trans. Automat. Control 11 2 1966 219 227
30. W. Zhang, and X. An Finite-time control of linear stochastic systems Int. J. Innovative Comput. Inform. Control 4 3 2008 689 696
31. F. Amato, R. Ambrosino, M. Ariola, and C. Cosentino Finite-time stability of linear time-varying systems with jumps Automatica 45 5 2009 1354 1358
32. F. Amato, M. Ariola, and C. Cosentino Finite-time control of discrete-time linear systems: analysis and design conditions Automatica 46 5 2010 919 924
33. G. Garcia, S. Tarbouriech, and J. Bernussou Finite-time stabilization of linear time-varying continuous systems IEEE Trans. Automat. Control 54 2 2009 364 369
34. infin control for linear continuous system with norm-bounded disturbance Commun. Nonlinear Sci. Numer. Simulat. 14 4 2009 1043 1049
35. Y. Yang, J.M. Li, and G.P. Chen Finite-time stability and stabilization of nonlinear stochastic hybrid systems J. Math. Anal. Appl. 356 3 2009 338 345
36. Y. Shen, and C. Li LMI-based finite-time boundedness analysis of neural networks with parametric uncertainties Neurocomputing 71 4-6 2008 502 507 (Pubitemid 351168438)
37. S. He, and F. Liu Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities Appl. Math. Model. 35 6 2011 2631 2638
38. infin finite-time control for switched systems with time-varying delay Nonlinear Anal. Hybrid Syst. 6 3 2012 885 898
39. infin control for a class of uncertain switched neutral systems Commun. Nonlinear Sci. Numer. Simulat. 17 4 2012 1766 1778
40. infin control of singular stochastic systems via static output feedback Appl. Math. Comput. 218 9 2012 5629 5640
41. Y. Zhang, C. Liu, and X. Mu Robust finite-time stabilization of uncertain singular Markovian jump systems Appl. Math. Model. 36 10 2012 5109 5121
42. F. Amato, and M. Ariola Finite-time control of discrete-time linear systems IEEE Trans. Automat. Control 50 5 2005 724 729 (Pubitemid 40784451)
43. F. Amato, M. Ariola, and P. Dorato Finite-time stabilization via dynamic output feedback Automatica 42 2 2006 337 342 (Pubitemid 41828195)
44. L 2-gain analysis for switched delay systems with norm-bounded disturbance Appl. Math. Comput. 217 12 2011 5982 5993
45. S. He, and F. Liu Observer-based finite-time control of time-delayed jump systems Appl. Math. Comput. 217 6 2010 2327 2338
46. Y. Zhang, C. Liu, X. Mu, and X. Guo Comment on "Observer-based finite-time control of time-delay jump systems" Appl. Math. Comput. 218 17 2012 9027 9032
47. infin control: constant and time-varying delays Int. J. Control 76 1 2003 48 60
48. infin filtering for time-delayed switched Hopfield neural networks Int. J. Innovative Comput. Inform. Control 7 4 2011 1831 1844
49. K. Gu, V. Kharitonov, and J. Chen Stability of Time-Delay Systems 2003 Birkhauser Boston
50. l filtering for uncertain discrete-time switched system with mode-dependent time-varying delays Int. J. Innovative Comput. Inform. Control 7 5(A) 2011 2213 2224
51. L. Wu, J. Su, P. Shi, and J. Qiu A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems IEEE Trans. Syst. Man Cybern. B Cybern. 41 1 2011 273 286
52. L. Wu, J. Su, P. Shi, and J. Qiu Model approximation for discrete-time state-delay systems in the T-S fuzzy framework IEEE Trans. Fuzzy Syst. 19 2 2011 366 378
53. X. Su, P. Shi, L. Wu, Y. Song, A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay, IEEE Trans. Fuzzy Syst., http://dx.doi.org/10.1109/TFUZZ.2012.2196522.
54. L. Zhu, Y. Shen, and C. Li Finite-time control of discrete-time systems with time-varying exogenous disturbance Commun. Nonlinear Sci. Numer. Simulat. 14 2 2009 361 370
55. infin finite-time control of discrete-time systems with packet loss Math. Probl. Eng. 2012 2012 897481 (1-15)
56. S. Boyd, L.E. Ghaoui, E. Feron, and V. Balakrishnan Linear Matrix Inequality in Systems and Control Theory SIAM Studies in Applied Mathematics 1994 Society for Industrial and Applied Mathematics Philadelphia, PA, USA