On approximate controllability of non-autonomous measure driven systems with non-instantaneous impulse

Surendra Kumar

Applied Mathematics and Computation, 2023, vol. 441, issue C

Abstract: It is known that the systems without any restriction on their Zeno behavior are immersed in an enormous type of hybrid system. This article deals with the concept of approximate controllability for a non-autonomous measure-driven system enforced by not instantaneous impulse. A bunch of new sufficient hypotheses is created to justify the solvability and approximate controllability of the system. We apply the fixed point technique and the theory of Lebesgue–Stieltjes integral in the space of piecewise regulated functions. Moreover, the measured differential equations are the generalization of ordinary impulsive differential equations. Thus, our findings are more general than that found in the literature. Finally, an example is included that demonstrates the effectiveness of the developed theory.

Keywords: Approximate controllability; Measure driven evolution equation; Non-instantaneous impulse; Lebesgue–Stieltjes integral; Regulated functions; Fixed point theory (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007639

DOI: 10.1016/j.amc.2022.127695

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