Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution. (14th October 2020)

• Record Type: Journal Article
• Authors: Kumar, Surendra; Mohammad Abdal, Syed
• Is Part Of: IMA journal of mathematical control and information. Volume 38:Number 2(2021)
• Page Start: 552
• Page End: 575
• Publication Date: 2020-10-14
• Subjects: measure driven differential equations -- regulated functions -- fundamental solution -- Lebesgue–Stieltjes integral -- approximate controllability -- fixed point theory; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnaa026
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii's fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.