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

Exponential stabilisation of positive singular linear discrete-time delay systems with bounded control

Exponential stabilisation of positive singular linear discrete-time delay systems with bounded control

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.

Inspired by the results obtained in Liu et al. (2008, 2009), this study extends the constrained control problem to singular linear positive discrete-time systems with delay. By using the singular value decomposition approach, delay-dependent sufficient conditions for the regularity, causality, positivity and exponential stabilisation with a given decay rate of the system are established in terms of linear programming problem. A numerical example to demonstrate the effectiveness of the proposed method is given.

References

    1. 1)
      • 1. Campbell, S.L.V.: ‘Singular systems of differential equations’ (Research Notes in Mathematics, Pitman Advanced Publishing, Boston, USA, 1982).
    2. 2)
      • 2. Dai, L.: ‘Singular control systems’ (Springer, Berlin, 1989).
    3. 3)
      • 3. Lam, J., Xu, S.: ‘Robust control and filtering of singular systems’ (Springer, Berlin, 2006).
    4. 4)
      • 4. Thanh, N.T., Niamsup, P., Phat, V.N.: ‘Finite-time stability of singular nonlinear switched time-delay systems: a singular value decomposition approach’, J. Franklin Inst., 2017, 354, pp. 35023518.
    5. 5)
      • 5. Liu, X., Zhong, S., Ding, X.: ‘A Razumikhin approach to exponential admissibility of switched descriptor delayed systems’, Appl. Math. Model., 2014, 38, pp. 16471659.
    6. 6)
      • 6. Zhang, Y., Liu, C., Mu, X.: ‘Robust finite-time stabilization of uncertain singular Markovian jump systems’, Appl. Math. Model., 2012, 36, pp. 51095121.
    7. 7)
      • 7. Bru, R., Romero-Vivo, S.: ‘Positive systems’ (Springer, Berlin, 2009).
    8. 8)
      • 8. Farina, L., Rinaldi, S.: ‘Positive linear systems’ (Wiley, New York, 2000).
    9. 9)
      • 9. Kaczorek, T.: ‘Positive 1-D and 2-D systems’ (Springer, Berlin, 2002).
    10. 10)
      • 10. Leenheer, D.P., Aeyels, D.: ‘Stabilization of positive linear systems’, Syst. Control Lett., 2001, 44, pp. 861868.
    11. 11)
      • 11. Ebihara, Y., Peaucelle, D., Arzelier, D.: ‘LMI approach to linear positive system analysis and synthesis’, Syst. Control Lett., 2014, 63, pp. 5056.
    12. 12)
      • 12. Liu, X., Wang, L., Yu, W., et al: ‘Constrained control of positive discrete-time systems with delays’, IEEE Trans. Circuit Syst. II, Exp. Bri., 2008, 55, pp. 193197.
    13. 13)
      • 13. Liu, X.: ‘Constrained control of positive systems with delays’, IEEE Trans. Autom. Control, 2009, 47, pp. 19561960.
    14. 14)
      • 14. Ngoc, P.H.A., Tinh, C.T.: ‘Robust stability of positive linear time delay systems under time-varying perturbations’, Bull. Pol. Acad. Sci. Tech., 2015, 63, pp. 947954.
    15. 15)
      • 15. Rami, M.A., Napp, D.: ‘Characterization and stability of autonomous positive descriptor systems’, IEEE Trans. Autom. Control, 2012, 57, pp. 26682673.
    16. 16)
      • 16. Virnik, E.: ‘Stability analysis of positive descriptor systems’, Linear Algebra Appl., 2008, 429, pp. 26402659.
    17. 17)
      • 17. Zhang, D., Zhang, Q., Du, B.: ‘Positivity and stability of positive singular Markovian jump time-delay systems with partially unknown transition rates’, J. Franklin Inst., 2017, 354, pp. 627649.
    18. 18)
      • 18. Liu, T., Wu, B., Yunxu, T.: ‘Exponential stability of discrete-time linear singular positive time-delay systems’. In: Proc. of the 27th Chinese Control and Decision Conf., Qingdao, China, 23–25 May 2015, pp. 60696073.
    19. 19)
      • 19. Li, S., Xiang, Z.: ‘Stability, l1-gain and l-gain analysis for discrete-time positive switched singular delayed systems’, Appl. Math. Comput., 2016, 275, pp. 95106.
    20. 20)
      • 20. Cui, Y., Shen, J., Feng, Z., et al: ‘Stability analysis for positive singular systems with time-varying delays’, IEEE Trans. Autom. Control, 2018, 63, pp. 14871494.
    21. 21)
      • 21. Qi, W., Gao, X.: ‘State feedback controller design for singular positive Markovian jump systems with partly known transition rates’, Appl. Math. Lett., 2015, 46, pp. 111116.
    22. 22)
      • 22. Efimov, D., Polyakov, A., Richard, J.P.: ‘Interval observer design for estimation and control of time-delay descriptor systems’, Eur. J. Control, 2015, 23, pp. 2635.
    23. 23)
      • 23. Malloci, I., Daafouz, J.: ‘Stabilisation of polytopic singularly perturbed linear systems’, Int. J. Control, 2012, 85, pp. 135142.
    24. 24)
      • 24. Xu, S., Yang, C.: ‘Stabilization of discrete-time singular systems: a matrix inequality approach’, Automatica, 1999, 35, pp. 16131617.
    25. 25)
      • 25. Zhu, S., Li, Z., Zhang, C.: ‘Exponential stability analysis for positive systems with delays’, IET Control Theory Appl., 2012, 6, pp. 761767.
    26. 26)
      • 26. De la Sen, M.: ‘About the properties of excitability and transparency in positive systems with point delays’, Appl. Math. Model., 2008, 32, pp. 4060.
    27. 27)
      • 27. Hmamed, A., Rami, M.A., Benzaoui, A., et al: ‘Stabilization under constrained states and ontrols of positive systems with time delays’, Eur. J. Control, 2012, 2, pp. 182190.
    28. 28)
      • 28. Rami, M.A., Napp, D.: ‘Positivity of discrete singular systems and their stability: an LP-based approach’, Automatica, 2014, 50, pp. 8491.
    29. 29)
      • 29. Sau, N.H., Niamsup, P., Phat, V.N.: ‘Positivity and stability analysis for linear implicit difference delay equations’, Linear Algebra Appl., 2016, 510, pp. 2541.
    30. 30)
      • 30. Fernando, T.L., Phat, V.N., Trinh, H.M.: ‘Feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays’, Appl. Math. Model., 2013, 37, pp. 15801589.
    31. 31)
      • 31. Vanderbei, R.J.: ‘Linear programming’ (Foundations and Extensions, International Series in Operations Research & Management Science, New York, USA2001).
    32. 32)
      • 32. Langbort, C., Arneson, H.A.: ‘Linear programming approach to routing control in networks of constrained linear positive systems’, Automatica, 2012, 48, pp. 800807.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2018.5150
Loading

Related content

content/journals/10.1049/iet-cta.2018.5150
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address