Approximate controllability of impulsive differential equations with state-dependent delay

• Published in: International journal of control Vol. 83; no. 2; pp. 387 - 393
• Main Authors: Sakthivel, R., Anandhi, E.R.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.02.2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applied sciences; approximate controllability; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; nonlinear impulsive systems; state-dependent delay; Studies; Differential equation; Non linear control; Evolution equation; Functional analysis; Semigroup; Delay dependent system; Non linear system; Linear control; Modeling; Equations of state; Pulse response; Controllability; Delay time; State dependence
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207170903171348

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 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.