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Research Article | Open Access

Analysis of relative controllability and finite-time stability in nonlinear switched fractional impulsive systems

P. K. Lakshmi Priya1, K. Kaliraj1,2, Panumart Sawangtong2,3,4( )
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamil Nadu, India
Research group for fractional calculus theory and applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand
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Abstract

This article investigated a class of switched impulsive fractional control systems with delays occurring at different time instants in both the state and control input. First, we analyzed the state response behavior and established sufficient conditions ensuring the system's stability over a finite time horizon. Next, we demonstrated the system's relative controllability using the fixed-point approach. Finally, a numerical simulation was presented to validate the theoretical findings.

Keywords

fractional delay systemGronwall's inequalityLaplace transformfixed point theoremswitched systemfinite-time stabilityrelative controllability
CLC number: 34A08, 34K10, 34K37, 37C25

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 8095-8115
DOI: 10.3934/math.2025371

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Cite this article:
Lakshmi Priya PK, Kaliraj K, Sawangtong P. Analysis of relative controllability and finite-time stability in nonlinear switched fractional impulsive systems. AIMS Mathematics, 2025, 10(4): 8095-8115. https://doi.org/10.3934/math.2025371

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Received: 21 January 2025
Revised: 14 March 2025
Accepted: 25 March 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)