On generalized Popov theory for delay systems

Silviu-Iulian Niculescu; Vlad Ionescu; Dan Ivanescu; Luc Dugard; Jean-Michel Dion

Kybernetika (2000)

  • Volume: 36, Issue: 1, page [2]-20
  • ISSN: 0023-5954

Abstract

top
This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an 2 norm bound constraint on disturbance attenuation. Note that the proposed results extend similar ones proposed by some of the authors [inddl:98].

How to cite

top

Niculescu, Silviu-Iulian, et al. "On generalized Popov theory for delay systems." Kybernetika 36.1 (2000): [2]-20. <http://eudml.org/doc/33465>.

@article{Niculescu2000,
abstract = {This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an $\{\mathcal \{L\}\}_2$ norm bound constraint on disturbance attenuation. Note that the proposed results extend similar ones proposed by some of the authors [inddl:98].},
author = {Niculescu, Silviu-Iulian, Ionescu, Vlad, Ivanescu, Dan, Dugard, Luc, Dion, Jean-Michel},
journal = {Kybernetika},
keywords = {Popov generalized theory; delay system; memoryless state feedback control; Popov generalized theory; delay system; memoryless state feedback control},
language = {eng},
number = {1},
pages = {[2]-20},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On generalized Popov theory for delay systems},
url = {http://eudml.org/doc/33465},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Niculescu, Silviu-Iulian
AU - Ionescu, Vlad
AU - Ivanescu, Dan
AU - Dugard, Luc
AU - Dion, Jean-Michel
TI - On generalized Popov theory for delay systems
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 1
SP - [2]
EP - 20
AB - This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an ${\mathcal {L}}_2$ norm bound constraint on disturbance attenuation. Note that the proposed results extend similar ones proposed by some of the authors [inddl:98].
LA - eng
KW - Popov generalized theory; delay system; memoryless state feedback control; Popov generalized theory; delay system; memoryless state feedback control
UR - http://eudml.org/doc/33465
ER -

References

top
  1. Boyd S., Ghaoui L. El, Feron E., Balakrishnan V., Linear matrix inequalities in system and control theory, (SIAM Stud. Appl. Math. 15.) SIAM Publication, Philadelphia 1994 Zbl0816.93004MR1284712
  2. Dugard L., (eds.) E. I. Verriest, Stability and Control of Time–delay Systems, (Lecture Notes in Control and Inform. Sciences 228.) Springer–Verlag, London 1997 Zbl0901.00019MR1482570
  3. Doyle J. C., Glover K., Khargonekar P. P., Francis B. A., 10.1109/9.29425, IEEE Trans. Automat. Control 34 (1989), 831–847 (1989) MR1004301DOI10.1109/9.29425
  4. Halanay A., Ionescu V., 10.1016/0167-6911(93)90080-P, Systems Control Lett. 20 (1993), 1–6 (1993) Zbl0778.93097MR1198466DOI10.1016/0167-6911(93)90080-P
  5. Halanay A., Ionescu V., Time–Varying Discrete Linear Systems, Birkhäuser, Basel 1994 Zbl0799.93035MR1269542
  6. Hale J. K., Lunel S. M. Verduyn, Introduction to Functional Differential Equations (Appl, Math. Sciences 99.), Springer–Verlag, Berlin 1991 
  7. Ionescu V., Weiss M., Continuous and discrete-time Riccati theory: a Popov function approach, Linear Algebra Appl. 193 (1993), 173–209 (193) MR1240278
  8. Ionescu V., Oară C., Weiss M., Generalized Riccati Theory, Wiley, New York 1998 Zbl0915.34024
  9. Ionescu V., Niculescu S. I., Woerdeman H., On 2 memoryless control of time–delay systems, In: Proc. 36th IEEE Conf. Decision Control, San Diego 1997 
  10. Ionescu V., Niculescu S. I., Dion J. M., Dugard L., Li H., Generalized Popov theory applied to state–delayed systems, In: Proc. 4th IFAC Conf. System Structure and Control, Nantes 1998 Zbl0965.93083
  11. Ionescu V., Niculescu S. I., Dion J. M., Dugard L., Li H., Generalized Popov theory applied to state–delayed systems, In: Proc. 4th IFAC Conf. System Structure Control, Nantes 1998 Zbl0965.93083
  12. Kolmanovskii V. B., Myshkis A., Applied Theory of Functional Differential Equations, Kluwer, Dordrecht 1992 MR1256486
  13. Kolmanovskii V. B., Nosov V. R., Stability of Functional Differential Equations, Math. Science Engrg. 180, Academic Press, New York 1986 Zbl0593.34070MR0860947
  14. Kolmanovskii V. B., Richard J. P., Stability of some systems with distributed delays, European J. Automat. Control 31 (1997), 971–982 (1997) 
  15. Kolmanovskii V. B., Richard J. P., Tchangani A. Ph., Stability of linear systems with discrete–plus–distributed delays: Application to some model transformations, In: Mathematical Theory of Networks and Systems (MTNS’98), Padova 1998 
  16. Lee J. H., Kim S. W., Kwon W. H., 10.1109/9.273356, IEEE Trans. Automat. Control 39 (1994), 159–162 (1994) MR1258692DOI10.1109/9.273356
  17. Li H., Niculescu S. I., Dugard L., Dion J. M., Robust control for uncertain linear time–delay systems: A linear matrix inequality approach, Part I. In: Proc. 35th IEEE Conf. Decision Control, Kobe 1996 
  18. Li H., Niculescu S. I., Dugard L., Dion J. M., Robust control for uncertain linear time–delay systems: A linear matrix inequality approach with guaranteed α -stability, Part II. In: Proc. 35th IEEE Conf. Decision Control, Kobe 1996 
  19. Niculescu S. I., 10.1109/9.668850, IEEE Trans. Automat. Control 43 (1998), 739–743 (1998) MR1618043DOI10.1109/9.668850
  20. Niculescu S. I., Time–delay systems, Qualitative aspects on stability and stabilization (in French), Diderot Eds., ‘Nouveaux Essais’ Series, Paris 1997 Zbl1235.93006
  21. Niculescu S. I., Ionescu V., On delay–independent stability criteria: A matrix pencil approach, IMA J. Math. Control Inform. 1997 Zbl0886.93056MR1467584
  22. Niculescu S. I., Souza C. E. de, Dion J. M., Dugard L., Robust memoryless control for uncertain linear systems with time–varying delay, In: 3rd European Control Conf., Rome 1995, pp. 1814–1818 (1995) 
  23. Niculescu S. I., Ionescu V., Woerdeman H., On the Popov theory for some classes of time-delay systems: A matrix pencil approach, In: MTNS’98, Padova 1998 
  24. Niculescu S. I., Verriest E. I., Dugard L., Dion J. M., Stability and robust stability of time–delay systems: A guided tour, In: Stability and Control of Time–Delay Systems (L. Dugard and E. I. Verriest, eds., Lecture Notes in Control and Inform. Sciences 228). Springer–Verlag, London 1997, pp. 1–71 (1997) MR1482571
  25. Noldus E., 10.1080/0020718508961174, Internat. J. Control 41 (1985), 947–960 (1985) Zbl0566.93048MR0792919DOI10.1080/0020718508961174
  26. Oară C., 10.1007/BF02140690, Numer. Algorithms 7 (1994), 355–377 (1994) MR1283105DOI10.1007/BF02140690
  27. Răsvan V., Absolute Stability of Time–Delay Control Systems (in Russian), Nauka, Moscow 1983 
  28. Richard J.-P., Some trends and tools for the study of time delay systems, In: CESA’98 IMACS–IEEE Multiconference, Hammamet 1998, pp. 27–43 (1998) 
  29. Xie L., Souza C. E. de, Robust stabilization and disturbance attenuation for uncertain delay system, In: Proc. 2nd European Control Conf., Groningen 1993, pp. 667–672 (1993) 

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.