Finite time stability and relative controllability of second order linear differential systems with pure delay

Mengmeng Li; Michal Fečkan; JinRong Wang

Applications of Mathematics (2023)

  • Volume: 68, Issue: 3, page 305-327
  • ISSN: 0862-7940

Abstract

top
We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.

How to cite

top

Li, Mengmeng, Fečkan, Michal, and Wang, JinRong. "Finite time stability and relative controllability of second order linear differential systems with pure delay." Applications of Mathematics 68.3 (2023): 305-327. <http://eudml.org/doc/299384>.

@article{Li2023,
abstract = {We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.},
author = {Li, Mengmeng, Fečkan, Michal, Wang, JinRong},
journal = {Applications of Mathematics},
keywords = {finite time stability; relative controllability; second order; delayed matrix function},
language = {eng},
number = {3},
pages = {305-327},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite time stability and relative controllability of second order linear differential systems with pure delay},
url = {http://eudml.org/doc/299384},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Li, Mengmeng
AU - Fečkan, Michal
AU - Wang, JinRong
TI - Finite time stability and relative controllability of second order linear differential systems with pure delay
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 305
EP - 327
AB - We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.
LA - eng
KW - finite time stability; relative controllability; second order; delayed matrix function
UR - http://eudml.org/doc/299384
ER -

References

top
  1. Diblík, J., Fečkan, M., Pospíšil, M., 10.1007/s11253-013-0765-y, Ukr. Math. J. 65 (2013), 64-76. (2013) Zbl1283.34057MR3104884DOI10.1007/s11253-013-0765-y
  2. Diblík, J., Fečkan, M., Pospíšil, M., 10.1137/140953654, SIAM J. Control Optim. 52 (2014), 1745-1760. (2014) Zbl1295.93008MR3206982DOI10.1137/140953654
  3. Diblík, J., Khusainov, D. Y., Růžičková, M., 10.1137/070689085, SIAM J. Control Optim. 47 (2008), 1140-1149. (2008) Zbl1161.93004MR2407011DOI10.1137/070689085
  4. Elshenhab, A. M., Wang, X. T., 10.1016/j.amc.2021.126443, Appl. Math. Comput. 410 (2021), Article ID 126443, 13 pages. (2021) Zbl07425968MR4274895DOI10.1016/j.amc.2021.126443
  5. Fečkan, M., Wang, J., Zhou, Y., 10.1007/s10957-012-0174-7, J. Optim. Theory Appl. 156 (2013), 79-95. (2013) Zbl1263.93031MR3019302DOI10.1007/s10957-012-0174-7
  6. Gantmakher, F. R., Theory of Matrices, Nauka, Moskva (1988), Russian. (1988) Zbl0666.15002MR0986246
  7. Khusainov, D. Y., Diblík, J., Růžičková, M., Lukáčová, J., 10.1007/s11072-008-0030-8, Nonlinear Oscil., N.Y. 11 (2008), 276-285. (2008) Zbl1276.34055MR2510692DOI10.1007/s11072-008-0030-8
  8. Khusainov, D. Y., Shuklin, G. V., 10.1007/s10778-005-0079-3, Int. Appl. Mech. 41 (2005), 210-221. (2005) Zbl1100.34062MR2190935DOI10.1007/s10778-005-0079-3
  9. Lazarević, M. P., Spasić, A. M., 10.1016/j.mcm.2008.09.011, Math. Comput. Modelling 49 (2009), 475-481. (2009) Zbl1165.34408MR2483650DOI10.1016/j.mcm.2008.09.011
  10. Li, M., Wang, J., 10.1016/j.aml.2016.09.004, Appl. Math. Lett. 64 (2017), 170-176. (2017) Zbl1354.34130MR3564757DOI10.1016/j.aml.2016.09.004
  11. Li, M., Wang, J., 10.1016/j.amc.2017.11.063, Appl. Math. Comput. 324 (2018), 254-265. (2018) Zbl1426.34110MR3743671DOI10.1016/j.amc.2017.11.063
  12. Li, X., Yang, X., Song, S., 10.1016/j.automatica.2019.01.031, Automatica 103 (2019), 135-140. (2019) Zbl1415.93188MR3911637DOI10.1016/j.automatica.2019.01.031
  13. Liang, C., Wang, J., O'Regan, D., 10.14232/ejqtde.2017.1.47, Electron. J. Qual. Theory Differ. Equ. 2017 (2017), Article ID 47, 18 pages. (2017) Zbl1413.34256MR3661723DOI10.14232/ejqtde.2017.1.47
  14. Liang, C., Wang, J., O'Regan, D., 10.1016/j.aml.2017.09.015, Appl. Math. Lett. 77 (2018), 72-78. (2018) Zbl1462.34105MR3725232DOI10.1016/j.aml.2017.09.015
  15. Pospíšil, M., 10.1137/15M1024287, SIAM J. Control Optim. 55 (2017), 835-855. (2017) Zbl1368.34093MR3625799DOI10.1137/15M1024287
  16. Pospíšil, M., 10.3846/mma.2020.11194, Math. Model. Anal. 25 (2020), 303-322. (2020) Zbl1476.34143MR4116589DOI10.3846/mma.2020.11194
  17. Si, Y., Wang, J., Fečkan, M., 10.1016/j.amc.2020.125139, Appl. Math. Comput. 376 (2020), Article ID 125139, 24 pages. (2020) Zbl1475.93015MR4070317DOI10.1016/j.amc.2020.125139
  18. Wang, J., Fečkan, M., Zhou, Y., 10.4310/DPDE.2014.v11.n1.a4, Dyn. Partial Differ. Equ. 11 (2014), 71-87. (2014) Zbl1314.47117MR3194051DOI10.4310/DPDE.2014.v11.n1.a4
  19. Wu, G.-C., Baleanu, D., Zeng, S.-D., 10.1016/j.cnsns.2017.09.001, Commun. Nonlinear Sci. Numer. Simul. 57 (2018), 299-308. (2018) Zbl07263288MR3724839DOI10.1016/j.cnsns.2017.09.001
  20. You, Z., Wang, J., O'Regan, D., Zhou, Y., 10.1002/mma.5400, Math. Methods Appl. Sci. 42 (2019), 954-968. (2019) Zbl1410.34235MR3905829DOI10.1002/mma.5400

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.