http://iet.metastore.ingenta.com
1887

Stability of discrete-time delay Markovian jump systems with stochastic non-linearity and impulses

Stability of discrete-time delay Markovian jump systems with stochastic non-linearity and impulses

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The purpose of this study is to investigate the stability for a class of discrete-time delay Markovian jump systems with stochastic non-linearity and impulses. By using stochastic Lyapunov functionals, some new results are given. Impulse effects on the stability of the systems are revealed. Some examples together with their simulations are also presented to illustrate the effectiveness of the proposed results.

References

    1. 1)
      • 1. Blair, W.P.Jr, Sworder, D.D.: ‘Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria’, Int. J. Control, 1975, 21, (5), pp. 833841 (doi: 10.1080/00207177508922037).
    2. 2)
      • 2. Ji, Y., Chizeck, H.J.: ‘Controllability, observability and discrete-time Markovian jump linear quadratic control’, Int. J. Control, 1988, 48, (2), pp. 481498 (doi: 10.1080/00207178808906192).
    3. 3)
      • 3. Mariton, M.: ‘Jump linear systems in automatic control’ (Marcel Dekker, 1990).
    4. 4)
      • 4. Costa, O.L.V., Fragoso, M.D.: ‘Stability results for discrete-time linear systems with Markovian jumping parameters’, J. Math. Anal. Appl., 1993, 179, (1), pp. 154178 (doi: 10.1006/jmaa.1993.1341).
    5. 5)
      • 5. Mahmoud, M.S., Shi, P.: ‘Robust control for Markovian jump linear discrete-time systems with unknown nonlinearities’, IEEE Trans. Cir. Syst. I, 2002, 49, (4), pp. 538542 (doi: 10.1109/81.995674).
    6. 6)
      • 6. de Souza, C.E.: ‘Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems’, IEEE Trans. Autom. Control, 2006, 51, (5), pp. 836841 (doi: 10.1109/TAC.2006.875012).
    7. 7)
      • 7. Lee, J., Khargonekar, P.P.: ‘Optimal output regulation for discrete-time switched and Markovian jump linear systems’, SIAM J. Control Optim., 2008, 47, (1), pp. 4072 (doi: 10.1137/060662290).
    8. 8)
      • 8. Raouf, J., Boukas, E.: ‘Stabilisation of singular Markovian jump systems with discontinuities and saturating inputs’, IET Control Theory Appl., 2009, 3, (7), pp. 971982 (doi: 10.1049/iet-cta.2007.0451).
    9. 9)
      • 9. Todorov, M.G., Fragoso, M.D.: ‘On the robust stability, stabilization, and stability radii of continuous-time infinite Markov jump linear systems’, SIAM J. Control Optim., 2011, 49, (3), pp. 11711196 (doi: 10.1137/090774410).
    10. 10)
      • 10. Yue, D., Han, Q.: ‘Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching’, IEEE Trans. Autom. Control, 2005, 50, (2), pp. 217222 (doi: 10.1109/TAC.2004.841935).
    11. 11)
      • 11. Cao, Y., Lam, J.: ‘Stochastic stabilizability and H control for discrete-time jump linear systems with time delay’, J. Franklin Inst., 1999, 336, (8), pp. 12631281 (doi: 10.1016/S0016-0032(99)00035-6).
    12. 12)
      • 12. Shi, P., Boukas, E.K., Agarwal, R.K.: ‘Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay’, IEEE Trans. Autom. Control, 1999, 44, (11), pp. 21392144 (doi: 10.1109/9.802932).
    13. 13)
      • 13. Boukas, E.K., Liu, Z.K.: ‘Robust H control of discrete-time Markovian jump linear systems with mode-dependent time-delays’, IEEE Trans. Autom. Control, 2001, 46, (12), pp. 19181924 (doi: 10.1109/9.975476).
    14. 14)
      • 14. Wang, Z., Lam, J., Liu, X.: ‘Robust filtering for discrete-time Markovian jump delay systems’, IEEE Signal Process. Lett., 2004, 11, (8), pp. 659662 (doi: 10.1109/LSP.2004.831729).
    15. 15)
      • 15. Liu, Y., Wang, Z., Wang, W.: ‘Reliable H filtering for discrete time-delay Markovian jump systems with partly unknown transition probabilities’, Int. J. Adapt. Control Signal Process., 2011, 25, (6), pp. 554570 (doi: 10.1002/acs.1231).
    16. 16)
      • 16. Mahmoud, M.S., Shi, P., Ismail, A.: ‘Robust H filtering for a class of linear jumping discrete-time delay systems’, Dyn. Contin. Discrete, Impulsive Syst. B, 2003, 10, (5), pp. 647662.
    17. 17)
      • 17. Mahmoud, M.S., Shi, P.: ‘Control of Markovian jump uncertain discrete time-delay systems by guaranteed cost approach’, Int. J. Hybrid Intell. Syst., 2003, 3, (2–3), pp. 217236.
    18. 18)
      • 18. Mahmoud, M.S., Shi, P.: ‘Methodologies for control of jumping time-delay systems’ (Kluwer Academic, Amsterdam, 2003, 1st edn.).
    19. 19)
      • 19. Li, H., Chen, B., Zhou, Q., Qian, W.: ‘Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2009, 39, (1), pp. 94102 (doi: 10.1109/TSMCB.2008.2002812).
    20. 20)
      • 20. Zhang, L., Boukas, E.K., Lam, J.: ‘Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities’, IEEE Trans. Autom. Control, 2008, 53, (10), pp. 24582464 (doi: 10.1109/TAC.2008.2007867).
    21. 21)
      • 21. Zhang, L., Boukas, E.K.: ‘Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities’, Automatica, 2009, 45, (2), pp. 463468 (doi: 10.1016/j.automatica.2008.08.010).
    22. 22)
      • 22. Zhang, L., Boukas, E.K.: ‘Mode-dependent H filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities’, Automatica, 2009, 45, (6), pp. 14621467 (doi: 10.1016/j.automatica.2009.02.002).
    23. 23)
      • 23. Costa, O.L.V., Fragoso, M.D., Marques, R.P.: ‘Discrete time Markov jump linear systems’ (Springer, 2005, 1st edn.).
    24. 24)
      • 24. Pan, S., Sun, J., Zhao, S.: ‘Stabilization of discrete-time Markovian jump linear systems via time-delayed and impulsive controllers’, Automatica, 2008, 44, (11), pp. 29542958 (doi: 10.1016/j.automatica.2008.04.004).
    25. 25)
      • 25. Mahmoud, M.S., Shi, P., Ismail, A.: ‘Robust Kalman filtering for discrete-time Markovian jump systems with parameter uncertainty’, J. Comput. Appl. Math., 2004, 169, (1), pp. 5369 (doi: 10.1016/j.cam.2003.11.002).
    26. 26)
      • 26. Sworder, D., Rogers, R.: ‘An LQ-solution to a control problem associated with a solar thermal central receiver’, IEEE Trans. Autom. Control, 1983, 28, (10), pp. 971978 (doi: 10.1109/TAC.1983.1103151).
    27. 27)
      • 27. Huang, L., Mao, X.: ‘On input-to-state stability of stochastic retarded systems with Markovian switching’, IEEE Trans. Autom. Control, 2009, 54, (8), pp. 18981902 (doi: 10.1109/TAC.2009.2022112).
    28. 28)
      • 28. Li, X., Gao, H., Yu, X.: ‘A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays’, IEEE Trans. Syst. Man Cybern. B: Cybern., 2011, 41, (5), pp. 12751286 (doi: 10.1109/TSMCB.2011.2125950).
    29. 29)
      • 29. Li, X., Gao, H.: ‘A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis’, IEEE Trans. Autom. Control, 2011, 56, (9), pp. 21722178 (doi: 10.1109/TAC.2011.2146850).
    30. 30)
      • 30. Gao, H., Li, X.: ‘H filtering for discrete-time state-delayed systems with finite frequency specifications’, IEEE Trans. Autom. Control, 2011, 56, (12), pp. 29352941 (doi: 10.1109/TAC.2011.2159909).
    31. 31)
      • 31. Hu, J., Wang, Z., Shen, B., Gao, H.: ‘Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays’, IEEE Trans. Signal Process., 2013, 61, (5), pp. 12301238 (doi: 10.1109/TSP.2012.2232660).
    32. 32)
      • 32. Li, C., Ma, F., Feng, G.: ‘Hybrid impulsive and switching time-delay systems’, IET Control Theory Appl., 2009, 3, (11), pp. 14871498 (doi: 10.1049/iet-cta.2008.0222).
    33. 33)
      • 33. Liu, B., Hill, D.J.: ‘Uniform stability of large-scale delay discrete impulsive systems’, Int. J. Control, 2009, 82, (2), pp. 228240 (doi: 10.1080/00207170802050809).
    34. 34)
      • 34. Zhang, Y., Sun, J., Feng, G.: ‘Impulsive control of discrete systems with time delay’, IEEE Trans. Autom. Control, 2009, 54, (4), pp. 830834 (doi: 10.1109/TAC.2008.2010968).
    35. 35)
      • 35. Zhang, Y.: ‘Exponential stability of impulsive discrete systems with time delays’, Appl. Math. Lett., 2012, 25, (12), pp. 22902297 (doi: 10.1016/j.aml.2012.06.019).
    36. 36)
      • 36. Zhang, Y., Feng, G., Sun, J.: ‘Stability of impulsive piecewise linear systems’, Int. J. Syst. Sci., 2013, 44, (1), pp. 139150 (doi: 10.1080/00207721.2011.598957).
    37. 37)
      • 37. Lakshmikantham, V., Bainov, D., Simeonov, P.S.: ‘Theory of impulsive differential equations’ (World Scientific, 1989).
    38. 38)
      • 38. Liu, Y., Zhao, S.: ‘Controllability for a class of linear time-varying impulsive systems with time delay in control input’, IEEE Trans. Autom. Control, 2011, 56, (2), pp. 395399 (doi: 10.1109/TAC.2010.2088811).
    39. 39)
      • 39. Xu, J., Sun, J.: ‘Finite-time stability of linear time-varying singular impulsive systems’, IET Control Theory Appl., 2010, 4, (10), pp. 22392244 (doi: 10.1049/iet-cta.2010.0242).
    40. 40)
      • 40. Antunes, D., Hespanha, J., Silvestre, C.: ‘Stability of networked control systems with asynchronous renewal links: an impulsive systems approach’, Automatica, 2013, 49, (2), pp. 402413 (doi: 10.1016/j.automatica.2012.11.033).
    41. 41)
      • 41. Jacobson, D.: ‘A general result in stochastic optimal control of nonlinear discrete-time systems with quadratic performance criteria’, J. Math. Anal. Appl., 1974, 47, (1), pp. 153161 (doi: 10.1016/0022-247X(74)90043-2).
    42. 42)
      • 42. Yaz, E., Yaz, Y.: ‘State estimation of uncertain nonlinear stochastic systems with general criteria’, Appl. Math. Lett., 2001, 14, (5), pp. 605610 (doi: 10.1016/S0893-9659(00)00201-9).
    43. 43)
      • 43. Wei, G., Wang, Z., Shu, H.: ‘Robust filtering with stochastic nonlinearities and multiple missing measurements’, Automatica, 2009, 45, (3), pp. 836841 (doi: 10.1016/j.automatica.2008.10.028).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0444
Loading

Related content

content/journals/10.1049/iet-cta.2013.0444
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address