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

P. K. Lakshmi Priya; K. Kaliraj; Panumart Sawangtong; P. K. Lakshmi Priya; K. Kaliraj; Panumart Sawangtong

doi:10.3934/math.2025371

AIMS Mathematics

2025, Volume 10, Issue 4: 8095-8115. doi: 10.3934/math.2025371

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

1.
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamil Nadu, India
2.
Research group for fractional calculus theory and applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand
3.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
4.
Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand

Received: 21 January 2025 Revised: 14 March 2025 Accepted: 25 March 2025 Published: 07 April 2025
MSC : 34A08, 34K10, 34K37, 37C25

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.
- fractional delay system,
- Gronwall's inequality,
- Laplace transform,
- fixed point theorem,
- switched system,
- finite-time stability,
- relative controllability
Citation: P. K. Lakshmi Priya, K. Kaliraj, Panumart Sawangtong. Analysis of relative controllability and finite-time stability in nonlinear switched fractional impulsive systems[J]. AIMS Mathematics, 2025, 10(4): 8095-8115. doi: 10.3934/math.2025371

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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.

References

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