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

Dwell-time approach to ℒ2-induced gain analysis of discrete-time switched systems subject to actuator saturation

Dwell-time approach to ℒ2-induced gain analysis of discrete-time switched systems subject to actuator saturation

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.

This study investigates ℒ2-induced gain from the input disturbance to output of discrete-time switched linear systems subject to actuator saturation. With the state feedback gains adopted beforehand, the authors establish the linear matrix inequalities formulation which estimates the restricted ℒ2-induced gain for this class of switched systems by dwell-time approach. Then the authors investigate the influence of parameter variations on the restricted ℒ2-induced gain, and present a state feedback design method for a fixed dwell time and an upper bound of restricted ℒ2-induced gain. In addition, the authors investigate the qualitative relationship between disturbances rejection capability and dwell time. A numerical example is provided to illustrate the effectiveness of our obtained results.

References

    1. 1)
      • 1. Liberzon, D.: ‘Switching in systems and control’ (Birkhäuser, 2003).
    2. 2)
      • 2. Sun, Z., Ge, S.S.: ‘Switched linear systems: control and design’ (Springer-Verlag, 2005).
    3. 3)
      • 3. Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C.: ‘Stability criteria for switched and hybrid systems’, SIAM Rev., 2007, 49, (4), pp. 545592.
    4. 4)
      • 4. Lin, H., Antsaklis, P.J.: ‘Stability and stabilizability of switched linear systems: a survey of recent results’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 308322.
    5. 5)
      • 5. Zhai, S., Yang, X.S.: ‘Stability analysis of feedback switched systems with state and switching delays’, IMA J. Math. Control Inf., 2012, doi:10.1093/imamci/dns010.
    6. 6)
      • 6. Dehghan, M., Ong, C.J., Chen, C.Y.: ‘Characterization and computation of robust invariant sets for switching systems under dwell-time consideration’. Proc. 50th IEEE Conf. Decision and Control and European Control Conf., Orlando, USA, 2011, pp. 11661171.
    7. 7)
      • 7. Dehghan, M., Ong, C.J.: ‘Discrete-time switching linear system with constraints: characterization and computation of invariant sets under dwell-time consideration’, Automatica, 2012, 48, (5), pp. 964969.
    8. 8)
      • 8. Zhang, L., Shi, P., Basin, M.: ‘Robust stability and stabilisation of uncertain switched linear discrete time-delay systemsIET Proc., Control Theory Appl., 2008, 2, (7), pp. 606614.
    9. 9)
      • 9. Zhai, G., Hu, B., Yasuda, K., Michel, A.N.: ‘Qualitative analysis of discrete-time switched systems’. Proc. American Control Conf., Orlando, USA, 2002, pp. 18801885.
    10. 10)
      • 10. Wu, A.G., Feng, G., Duan, G.R., Gao, H.: ‘Stabilising slow-switching laws for switched discrete-time linear systems’, IET Proc., Control Theory Appl., 2011, 5, (16), pp. 18431858.
    11. 11)
      • 11. Ding, D.W., Yang, G.H.: ‘H static output feedback control for discrete-time switched linear systems with average dwell time’, IET Proc., Control Theory Appl., 2010, 4, (3), pp. 381390.
    12. 12)
      • 12. van der Schaft, A.J.: ‘2-Gain and passivity techniques in nonlinear control’ (Springer-Verlag, 2000, 2nd edn.).
    13. 13)
      • 13. Zhai, G., Hu, B., Yasuda, K., Michel, A.N.: ‘Disturbance attenuation properties of time-controlled switched systems’, J. Franklin Inst., 2001, 338, pp. 765779.
    14. 14)
      • 14. Xie, D., Wang, L., Hao, F., Xie, G.: ‘LMI approach to ℒ2 gain analysis and control synthesis of uncertain switched systems’, IEE Proc., Control Theory Appl., 2004, 151, (1), pp. 2128.
    15. 15)
      • 15. Roberson, D.G., Stilwell, D.J.: ‘2 gain of periodic linear switched systems: fast switching behavior’, IEEE Trans. Autom. Control, 2009, 54, (7), pp. 16321637.
    16. 16)
      • 16. Zhao, J., Hill, D.J.: ‘On stability and ℒ2 gain and H control for switched systems’, Automatica, 2008, 44, pp. 12201232.
    17. 17)
      • 17. Hespanha, J.P.: ‘2-induced gains of switched linear systems’, in Blondel, V., Megretski, A., (Eds.): ‘Unsolved problems in mathematical systems and control theory’ (Princeton University Press, 2004), pp. 131133.
    18. 18)
      • 18. Hespanha, J.P.: ‘Root-mean-square gains of switched linear systems’, IEEE Trans. Autom. Control, 2003, 48, (11), pp. 20402045.
    19. 19)
      • 19. Margaliot, M., Hespanha, J.P.: ‘Root-mean-square gains of switched linear systems: a variational approach’, Automatica, 2008, 44, (9), pp. 23982402.
    20. 20)
      • 20. Hirata, K., Hespanha, J.P.: ‘2-induiced gain analysis for a class of switched systems’. Proc. 48th IEEE Conf. Decision and Control, Shanghai, China, 2009, pp. 21382143.
    21. 21)
      • 21. Hirata, K., Hespanha, J.P.: ‘2-induiced gain analysis of switched linear systems via finitely parameterized storage functions’. Proc. American Control Conf., Baltimore, USA, 2010, pp. 40644069.
    22. 22)
      • 22. Geromel, J.C., Colaneri, P.: ‘H and dwell time specifications of continuous-time switched linear systems’, IEEE Trans. Autom. Control, 2010, 55, (1), pp. 207212.
    23. 23)
      • 23. Lee, J., Dullerud, G.E.: ‘Optimal disturbance attenuation for discrete-time switched and Markovian jump linear systems’, SIAM J. Control Optim., 2006, 45, (4), pp. 1329C1358.
    24. 24)
      • 24. Colaneri, P., Bolzern, P., Geromel, J.C.: ‘Root mean square gain of discrete-time switched linear systems under dwell time constraints’, Automatica, 2011, 47, (8), pp. 16771684.
    25. 25)
      • 25. Cai, C.: ‘Dwell-time approach to input-output stability properties for a class of discrete-time dynamical systems’, Syst. Control Lett., 2011, 60, pp. 383389.
    26. 26)
      • 26. Hu, T., Lin, Z.: ‘Control systems with actuator saturation: analysis and design’ (Birkhäuser, 2001).
    27. 27)
      • 27. Hu, T., Lin, Z., Chen, B.M.: ‘Analysis and design for discrete-time linear systems subject to actuator saturation’, Syst. Control Lett., 2002, 45, (2), pp. 97112.
    28. 28)
      • 28. Wada, N., Oomoto, T., Saeki, M.: ‘2-gain analysis of discrete-time systems with saturation nonlinearity using parameter dependent Lyapunov function’. Proc. 43th IEEE Conf. Decision and Control, Atlantis, Paradise Island, Bahamas, 2004, pp. 19521957.
    29. 29)
      • 29. Soodavi, M., Ghaisari, J., Sheikholeslam, F.: ‘2 gain analysis for switched systems with state-dependent switching signal’, IET Proc., Control Theory Appl., 2011, 5, (13), pp. 15231527.
    30. 30)
      • 30. Ma, Y.M., Yang, G.H.: ‘Disturbance rejection of switched discrete-time systems with saturation nonlinearity’. Proc. 46th IEEE Conf. Decision and Control, New Orleans, USA, 2007, pp. 31703175.
    31. 31)
      • 31. Zhang, X., Zhao, J., Dimirovski, G.M.: ‘2-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation’, Int. J. Control, 2011, 84, (10), pp. 17461758.
    32. 32)
      • 32. Zhang, X., Zhao, J., Dimirovski, G.M.: ‘2-gain analysis and control synthesis of uncertain switched linear systems subject to actuator saturation’, Int. J. Syst. Sci., 2012, 43, (4), pp. 731740.
    33. 33)
      • 33. Ni, W., Cheng, D.: ‘Control of switched linear systems with input saturation’, Int. J. Syst. Sci., 2010, 41, (9), pp. 10571065.
    34. 34)
      • 34. Benzaouia, A., Akhrif, O., Saydy, L.: ‘Stabilisation and control synthesis of switching systems subject to actuator saturation’, Int. J. Syst. Sci., 2010, 41, (4), pp. 397409.
    35. 35)
      • 35. Benzaouia, A., Saydy, L., Akhrif, O.: ‘Stability and control synthesis of switched systems subject to actuator saturation’. Proc. American Control Conf., Boston, USA, 2004, pp. 58185823.
    36. 36)
      • 36. Chen, Y., Fei, S., Zhang, K., Yu, L.: ‘Control of switched linear systems with actuator saturation and its applications’, Math. Comput. Model., 2012, 56, (1–2), pp. 1426.
    37. 37)
      • 37. Chen, Y., Fei, S., Zhang, K., Fu, Z.: ‘Control synthesis of discrete-time switched linear systems with input saturation based on minimum dwell time approach’, Circuits Syst. Signal Process., 2012, 31, (2), pp. 779795.
    38. 38)
      • 38. Lu, L., Lin, Z.: ‘Design of switched linear systems in the presence of actuator saturation’, IEEE Trans. Autom. Control, 2008, 53, (6), pp. 15361542.
    39. 39)
      • 39. Lu, L., Lin, Z., Fang, H.: ‘2 gain analysis for a class of switched systems’, Automatica, 2009, 45, (4), pp. 965972.
    40. 40)
      • 40. Rugh, W.J.: Linear systems theory (Prentice-Hall, 1996, 2nd edn.).
    41. 41)
      • 41. Löfberg, J.: ‘YALMIP: a toolbox for modeling and optimization in MATLAB’. Proc. CACSD Conf., Taipei, Taiwan, 2004, pp. 284289.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2012.0508
Loading

Related content

content/journals/10.1049/iet-cta.2012.0508
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address