Approximate controllability of impulsive differential equations with state-dependent delay. (English) Zbl 1184.93021

Sakthivel, R.; Anandhi, E. R.

Int. J. Control 83, No. 2, 387-393 (2010).

Summary: In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations have been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive differential equations with state-dependent delay is investigated. We study the approximate controllability for a nonlinear impulsive differential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

MSC:

93B05	Controllability
93C15	Control/observation systems governed by ordinary differential equations
34A37	Ordinary differential equations with impulses

Keywords:

approximate controllability; nonlinear impulsive systems; state-dependent delay

References:

[1]	DOI: 10.1016/j.mbs.2005.03.012 · Zbl 1071.92013
[2]	DOI: 10.1016/S0025-5564(98)00008-X · Zbl 0938.92028
[3]	DOI: 10.1023/A:1016031617252 · Zbl 1051.93014
[4]	DOI: 10.1006/jmaa.2000.7234 · Zbl 0982.93018
[5]	DOI: 10.1016/S0362-546X(03)00041-5 · Zbl 1037.34061
[6]	DOI: 10.4171/ZAA/1291 · Zbl 1101.93007
[7]	DOI: 10.1016/j.jmaa.2006.10.084 · Zbl 1115.93015
[8]	DOI: 10.1016/j.chaos.2006.03.006 · Zbl 1136.93006
[9]	DOI: 10.1016/j.na.2006.06.018 · Zbl 1128.93005
[10]	DOI: 10.1016/S0022-247X(02)00225-1 · Zbl 1017.93019
[11]	DOI: 10.1016/j.vaccine.2006.05.018
[12]	DOI: 10.1016/j.chaos.2005.05.027 · Zbl 1079.92036
[13]	DOI: 10.1016/S0034-4877(05)80096-5 · Zbl 1185.93016
[14]	Hernandez E, Electronic Journal of Differential Equations 28 pp 11– (2008)
[15]	Hino Y, Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics 1473 (1991) · Zbl 0732.34051
[16]	DOI: 10.1016/j.na.2005.02.118 · Zbl 1077.93005
[17]	DOI: 10.1016/j.chaos.2005.08.041 · Zbl 1110.34057
[18]	DOI: 10.1016/j.na.2004.11.022 · Zbl 1079.93008
[19]	DOI: 10.1006/jtbi.1997.0537
[20]	DOI: 10.1137/S0363012901391688 · Zbl 1084.93006
[21]	DOI: 10.1016/j.na.2006.11.018 · Zbl 1129.93004
[22]	DOI: 10.1007/BF00938799 · Zbl 0632.93007
[23]	DOI: 10.1016/j.mcm.2004.03.007 · Zbl 1129.93005
[24]	DOI: 10.1007/s002850100121 · Zbl 0990.92033