Robust Observer-based control of switched nonlinear systems with quantized and sampled output

Carlos Perez; Manuel Mera

Kybernetika (2015)

  • Volume: 51, Issue: 1, page 59-80
  • ISSN: 0023-5954

Abstract

top
This paper deals with the robust stabilization of a class of nonlinear switched systems with non-vanishing bounded perturbations. The nonlinearities in the systems satisfy a quasi-Lipschitz condition. An observer-based linear-type switching controller with quantized and sampled output signal is considered. Using a dwell-time approach and an extended version of the invariant ellipsoid method (IEM) sufficient conditions for stability in a practical sense are derived. These conditions are represented as Bilinear Matrix Inequalities (BMI's). Finally, two examples are given to verify the efficiency of the proposed method.

How to cite

top

Perez, Carlos, and Mera, Manuel. "Robust Observer-based control of switched nonlinear systems with quantized and sampled output." Kybernetika 51.1 (2015): 59-80. <http://eudml.org/doc/270051>.

@article{Perez2015,
abstract = {This paper deals with the robust stabilization of a class of nonlinear switched systems with non-vanishing bounded perturbations. The nonlinearities in the systems satisfy a quasi-Lipschitz condition. An observer-based linear-type switching controller with quantized and sampled output signal is considered. Using a dwell-time approach and an extended version of the invariant ellipsoid method (IEM) sufficient conditions for stability in a practical sense are derived. These conditions are represented as Bilinear Matrix Inequalities (BMI's). Finally, two examples are given to verify the efficiency of the proposed method.},
author = {Perez, Carlos, Mera, Manuel},
journal = {Kybernetika},
keywords = {switched systems; robust stabilization; quantization; switched systems; robust stabilization; quantization},
language = {eng},
number = {1},
pages = {59-80},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust Observer-based control of switched nonlinear systems with quantized and sampled output},
url = {http://eudml.org/doc/270051},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Perez, Carlos
AU - Mera, Manuel
TI - Robust Observer-based control of switched nonlinear systems with quantized and sampled output
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 1
SP - 59
EP - 80
AB - This paper deals with the robust stabilization of a class of nonlinear switched systems with non-vanishing bounded perturbations. The nonlinearities in the systems satisfy a quasi-Lipschitz condition. An observer-based linear-type switching controller with quantized and sampled output signal is considered. Using a dwell-time approach and an extended version of the invariant ellipsoid method (IEM) sufficient conditions for stability in a practical sense are derived. These conditions are represented as Bilinear Matrix Inequalities (BMI's). Finally, two examples are given to verify the efficiency of the proposed method.
LA - eng
KW - switched systems; robust stabilization; quantization; switched systems; robust stabilization; quantization
UR - http://eudml.org/doc/270051
ER -

References

top
  1. Aihara, K., Suzuki, H., 10.1098/rsta.2010.0237, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 368 (2010), 4893-4914. Zbl1211.37099DOI10.1098/rsta.2010.0237
  2. Azhmyakov, V., 10.1109/cdc.2011.6161180, In: Proc. 50th IEEE Conference on Decision and Control and demonstratedntrol Conference, Orlando 2011, pp. 1353-1358. DOI10.1109/cdc.2011.6161180
  3. Balluchi, A., Benvenuti, L., Benedetto, M. D. Di, Sangiovanni-Vincentelli, A., 10.1016/j.automatica.2013.01.037, Automatica 49 (2013), 915-925. Zbl1284.93155MR3029107DOI10.1016/j.automatica.2013.01.037
  4. Yazdi, M. Barkhordari, Jahed-Motlagh, M. R., 10.1016/j.cej.2009.09.008, Chemical Engrg. J. 155 (2009), 838-843. DOI10.1016/j.cej.2009.09.008
  5. Blanchini, F., Miani, S., 10.1007/978-0-8176-4606-6_9, Birkhauser, Boston 2008. Zbl1140.93001MR2359816DOI10.1007/978-0-8176-4606-6_9
  6. Branicky, M., 10.1109/tac.2012.2199169, IEEE Trans. Automat. Control 57 (1998), 3038-3050. Zbl0904.93036MR1617575DOI10.1109/tac.2012.2199169
  7. Donkers, M. C. F., Hemmels, W. P. M. H., Wouw, N. Van den, Hetel, L., 10.1109/tac.2011.2107631, IEEE Trans. Automat. Control 56 (2011), 9, 2101-2115. MR2865767DOI10.1109/tac.2011.2107631
  8. Filipov, A. F., Differential Equations with Discontinuous Right-hand Side., Kluwer, Dordrecht 1988. 
  9. Fridman, E., 10.1109/tac.2006.872828, IEEE Trans. Automat. Control 51 (2006), 890-897. MR2232620DOI10.1109/tac.2006.872828
  10. Fridman, E., Niculescu, S. I., 10.1002/rnc.1230, Int. J. Robust Nonlinear Control 18 (2008), 3, 364-374. Zbl1284.93206MR2378407DOI10.1002/rnc.1230
  11. Fridman, E., Dambrine, M., 10.1016/j.automatica.2009.05.020, Automatica 45 (2009), 10, 2258-2264. Zbl1179.93089MR2890785DOI10.1016/j.automatica.2009.05.020
  12. Fu, M., Xie, L., 10.1109/tac.2005.858689, IEEE Trans. Automat. Control 50 (2005), 11, 1698-1711. MR2182717DOI10.1109/tac.2005.858689
  13. Gao, H., Chen, T., 10.1016/j.automatica.2007.06.015, Automatica 44 (2008), 2, 534-542. Zbl1283.93131MR2530803DOI10.1016/j.automatica.2007.06.015
  14. Geromel, J. C., Colaneri, P., 10.1137/050646366, SIAM J. Control Optim. 45 (2006), 5, 1915-1930. Zbl1130.34030MR2272172DOI10.1137/050646366
  15. Glover, J. D., Schweppe, F. C., 10.1109/tac.1971.1099781, IEEE Trans. Automat. Control 16 (1971), 5, 411-423. MR0287947DOI10.1109/tac.1971.1099781
  16. Gonzalez-Garcia, S., Polyakov, A., Poznyak, A., 10.1109/ssst.2009.4806834, In: Proc. 41st Southeastern Symposium on System Theory 2009, pp. 195-198. DOI10.1109/ssst.2009.4806834
  17. Gonzalez-Garcia, S., Polyakov., A., Poznyak, A., 10.1109/acc.2009.5160434, In: American Control Conference, St. Louis 2009, pp. 1160-1165. DOI10.1109/acc.2009.5160434
  18. Hartman, P., 10.1137/1.9780898719222, Society for Industrial and Applied Mathematics, Philadelphia 2002. MR1929104DOI10.1137/1.9780898719222
  19. Hespanha, J. P., Morse, A. S., 10.1109/cdc.1999.831330, In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 2655-2660. DOI10.1109/cdc.1999.831330
  20. Kruszewski, A., Jiang, W. J., Fridman, E., Richard, J. P., Toguyeni, A., 10.1109/tcst.2011.2159793, IEEE Trans. Control Systems Technol. 20 (2012), 887-900. DOI10.1109/tcst.2011.2159793
  21. Khurzhanski, A. B., Varaiya, P., 10.1137/s0363012903437605, SIAM J. Control Optim. 45 (2006), 1369-1394. MR2257227DOI10.1137/s0363012903437605
  22. Li, J., Liu, Y., Mei, R., Li, B., 10.1109/wcica.2010.5553817, In: Proc. 8th World Congress on Intelligent Control and Automation 2010, pp. 3377-3382. DOI10.1109/wcica.2010.5553817
  23. Liberzon, D., 10.1007/978-1-4612-0017-8, In: Systems & Control. Foundations & Applications, Birkhauser, Boston 2003. Zbl1036.93001MR1987806DOI10.1007/978-1-4612-0017-8
  24. Liberzon, D., 10.1109/cdc.2011.6160212, In: Proc. 50th IEEE Conference on Decision and Control and European Control Conference, Orlando 2011, pp. 8321-8328. DOI10.1109/cdc.2011.6160212
  25. Liberzon, D., 10.1016/j.automatica.2013.11.037, Automatica 50 (2014), 2, 409-420. MR3163788DOI10.1016/j.automatica.2013.11.037
  26. Lin, H., Antsaklis, P. J., 10.1109/tac.2008.2012009, IEEE Trans. Automat. Control 54 (2009), 308-322. MR2491959DOI10.1109/tac.2008.2012009
  27. Liu, Y., Niu, Y., Ho, D., Sliding mode control for linear uncertain switched systems., In: Proc. 31st Chinese Control Conference, Hefei 2012, pp. 3177-3181. 
  28. Liu, T., Jiang, Z. P., Hill, D. J., 10.1109/tac.2012.2191870, IEEE Trans. Automat. Control 57 (2012),5, 1326-1332. MR2923898DOI10.1109/tac.2012.2191870
  29. Liu, T., Jiang, Z. P., Hill, D. J., 10.1016/j.automatica.2011.09.041, Automatica 48 (2012), 1, 145-152. Zbl1244.93066MR2879422DOI10.1016/j.automatica.2011.09.041
  30. Lozada-Castillo, N. B., Alazki, H., Poznyak, A. S., 10.1093/imamci/dns008, IMA J. Math. Control Inform. 30 (2013), 1-19. Zbl1273.93167MR3037694DOI10.1093/imamci/dns008
  31. Nair, G. N., Fagnani, F., Zampieri, S., Evans, R. J., 10.1109/jproc.2006.887294, Proc. of the IEEE 95 (2007), 108-137. DOI10.1109/jproc.2006.887294
  32. Nie, H., Song, Z., Li, P., Zhao, J., 10.1109/ccdc.2008.4598158, In: Proc. 2008 Chinese Control and Decision Conference, Yantai-Shandong 2008, pp. 4381-4386. DOI10.1109/ccdc.2008.4598158
  33. Ordaz, P., Alazki, H., Poznyak, A., A sample-time adjusted feedback for robust bounded output stabilization., Kybernetika 49 (2013), 6, 911-934. Zbl1284.93242MR3182648
  34. Peng, C., Tian, Y. C., 10.1016/j.ins.2007.05.025, Inform. Sci. 177 (2007), 5763-5774. Zbl1126.93338MR2362219DOI10.1016/j.ins.2007.05.025
  35. Polyak, B. T., Nazin, S. A., Durieu, C., Walter, E., 10.1016/j.automatica.2004.02.014, Automatica 40 (2004), 1171-1179. Zbl1056.93063MR2148312DOI10.1016/j.automatica.2004.02.014
  36. Polyak, B. T., Topunov, M. V., 10.1134/s000511790805007x, Autom. Remote Control 69 (2008), 801-818. Zbl1156.93338MR2437453DOI10.1134/s000511790805007x
  37. Poznyak, A. S., 10.1134/s0005117909110174, Elsevier, Amsterdam 2008. MR2374025DOI10.1134/s0005117909110174
  38. Poznyak, A. S., Azhmyakov, V., Mera, M., 10.1080/00207179.2011.603097, Int. J. Control 84 (2011), 1408-1416. MR2830870DOI10.1080/00207179.2011.603097
  39. Shorten, R., Wirth, F., Manson, O., Wulff, K., King, C., 10.1137/05063516x, SIAM Rev. 49 (2007), 545-592. MR2375524DOI10.1137/05063516x
  40. Sun, Z., Ge, S. S., 10.1007/978-0-85729-256-8, Springer-Verlag, London 2011. MR3221851DOI10.1007/978-0-85729-256-8
  41. Tatikonda, S., Mitter, S., 10.1109/tac.2004.831187, IEEE Trans. Automat. Control 49 (2004), 1056-1068. MR2071934DOI10.1109/tac.2004.831187
  42. Wang, Y., Gupta, V., Antsaklis, P., 10.1109/tac.2013.2287074, IEEE Trans. Automat. Control 59 (2014), 692-702. MR3188475DOI10.1109/tac.2013.2287074
  43. Yanyan, L., Jun, Z., Dimirovski, G., Passivity, feedback equivalence and stability of switched nonlinear systems using multiple storage functions., In: Proc. 30th Chinese Control Conference, Yantai 2011, pp. 1805-1809. 
  44. Zhang, W. A., Yu, L., 10.1109/tac.2007.904284, IEEE Trans. Automat. Control 52 (2007), 1705-1710. MR2352449DOI10.1109/tac.2007.904284

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.