Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
finite time stability; relative controllability; second order; delayed matrix function
finite time stability; relative controllability; second order; delayed matrix function
Summary:
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.
References:
[1] Diblík, J., Fečkan, M., Pospíšil, M.: Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices. Ukr. Math. J. 65 (2013), 64-76. DOI 10.1007/s11253-013-0765-y | MR 3104884 | Zbl 1283.34057
[2] Diblík, J., Fečkan, M., Pospíšil, M.: On the new control functions for linear discrete delay systems. SIAM J. Control Optim. 52 (2014), 1745-1760. DOI 10.1137/140953654 | MR 3206982 | Zbl 1295.93008
[3] Diblík, J., Khusainov, D. Y., Růžičková, M.: Controllability of linear discrete systems with constant coefficients and pure delay. SIAM J. Control Optim. 47 (2008), 1140-1149. DOI 10.1137/070689085 | MR 2407011 | Zbl 1161.93004
[4] Elshenhab, A. M., Wang, X. T.: Representation of solutions of linear differential systems with pure delay and multiple delays with linear parts given by non-permutable matrices. Appl. Math. Comput. 410 (2021), Article ID 126443, 13 pages. DOI 10.1016/j.amc.2021.126443 | MR 4274895 | Zbl 07425968
[5] Fečkan, M., Wang, J., Zhou, Y.: Controllability of fractional functional evolution equations of Sobolev type via characteristic solution operators. J. Optim. Theory Appl. 156 (2013), 79-95. DOI 10.1007/s10957-012-0174-7 | MR 3019302 | Zbl 1263.93031
[6] Gantmakher, F. R.: Theory of Matrices. Nauka, Moskva (1988), Russian. MR 0986246 | Zbl 0666.15002
[7] Khusainov, D. Y., Diblík, J., Růžičková, M., Lukáčová, J.: Representation of a solution of the Cauchy problem for an oscillating system with pure delay. Nonlinear Oscil., N.Y. 11 (2008), 276-285. DOI 10.1007/s11072-008-0030-8 | MR 2510692 | Zbl 1276.34055
[8] Khusainov, D. Y., Shuklin, G. V.: Relative controllability in systems with pure delay. Int. Appl. Mech. 41 (2005), 210-221. DOI 10.1007/s10778-005-0079-3 | MR 2190935 | Zbl 1100.34062
[9] Lazarević, M. P., Spasić, A. M.: Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach. Math. Comput. Modelling 49 (2009), 475-481. DOI 10.1016/j.mcm.2008.09.011 | MR 2483650 | Zbl 1165.34408
[10] Li, M., Wang, J.: Finite time stability of fractional delay differential equations. Appl. Math. Lett. 64 (2017), 170-176. DOI 10.1016/j.aml.2016.09.004 | MR 3564757 | Zbl 1354.34130
[11] Li, M., Wang, J.: Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations. Appl. Math. Comput. 324 (2018), 254-265. DOI 10.1016/j.amc.2017.11.063 | MR 3743671 | Zbl 1426.34110
[12] Li, X., Yang, X., Song, S.: Lyapunov conditions for finite-time stability of time-varying time-delay systems. Automatica 103 (2019), 135-140. DOI 10.1016/j.automatica.2019.01.031 | MR 3911637 | Zbl 1415.93188
[13] Liang, C., Wang, J., O'Regan, D.: Controllability of nonlinear delay oscillating systems. Electron. J. Qual. Theory Differ. Equ. 2017 (2017), Article ID 47, 18 pages. DOI 10.14232/ejqtde.2017.1.47 | MR 3661723 | Zbl 1413.34256
[14] Liang, C., Wang, J., O'Regan, D.: Representation of a solution for a fractional linear system with pure delay. Appl. Math. Lett. 77 (2018), 72-78. DOI 10.1016/j.aml.2017.09.015 | MR 3725232 | Zbl 1462.34105
[15] Pospíšil, M.: Relative controllability of neutral differential equations with a delay. SIAM J. Control Optim. 55 (2017), 835-855. DOI 10.1137/15M1024287 | MR 3625799 | Zbl 1368.34093
[16] Pospíšil, M.: Representation of solutions of systems of linear differential equations with multiple delays and nonpermutable variable coefficients. Math. Model. Anal. 25 (2020), 303-322. DOI 10.3846/mma.2020.11194 | MR 4116589 | Zbl 1476.34143
[17] Si, Y., Wang, J., Fečkan, M.: Controllability of linear and nonlinear systems governed by Stieltjes differential equations. Appl. Math. Comput. 376 (2020), Article ID 125139, 24 pages. DOI 10.1016/j.amc.2020.125139 | MR 4070317 | Zbl 1475.93015
[18] Wang, J., Fečkan, M., Zhou, Y.: Controllability of Sobolev type fractional evolution systems. Dyn. Partial Differ. Equ. 11 (2014), 71-87. DOI 10.4310/DPDE.2014.v11.n1.a4 | MR 3194051 | Zbl 1314.47117
[19] Wu, G.-C., Baleanu, D., Zeng, S.-D.: Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion. Commun. Nonlinear Sci. Numer. Simul. 57 (2018), 299-308. DOI 10.1016/j.cnsns.2017.09.001 | MR 3724839 | Zbl 07263288
[20] You, Z., Wang, J., O'Regan, D., Zhou, Y.: Relative controllability of delay differential systems with impulses and linear parts defined by permutable matrices. Math. Methods Appl. Sci. 42 (2019), 954-968. DOI 10.1002/mma.5400 | MR 3905829 | Zbl 1410.34235
Search
Partner of
