Hostile-based bipartite containment control of nonlinear fractional multi-agent systems with input delays: a signed graph approach under disturbance and switching networks

Asad Khan; Azmat Ullah Khan Niazi; Saadia Rehman; Sidra Ahmed; Asad Khan; Azmat Ullah Khan Niazi; Saadia Rehman; Sidra Ahmed

doi:10.3934/math.2024620

AIMS Mathematics

2024, Volume 9, Issue 5: 12678-12699. doi: 10.3934/math.2024620

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Hostile-based bipartite containment control of nonlinear fractional multi-agent systems with input delays: a signed graph approach under disturbance and switching networks

1.
Metaverse Research Institute, School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
2.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
3.
Department of Physics, The University of Lahore, Sargodha 40100, Pakistan

Received: 24 January 2024 Revised: 04 March 2024 Accepted: 08 March 2024 Published: 02 April 2024
MSC : 93A16, 93D50

This article addresses the hostile-based bipartite containment control of nonlinear fractional multi-agent systems (FMASs) with input delays. Several fundamental algebraic criteria have been offered by the use of signed graph theory. To make the controller design more realistic, we assumed that the controller was under some disturbance. For the analysis of bipartite containment control, we used a fixed and switching signed network. The commonly used Lyapunov function approach and the Razumikhin technique were used. The use of these techniques can conquer the challenge brought on by switching, temporal delays, and fractional mathematics. To better elucidate the theoretical results, two examples are provided.
- bipartite containment control,
- Lyapunov function,
- signed digraph,
- switching network
Citation: Asad Khan, Azmat Ullah Khan Niazi, Saadia Rehman, Sidra Ahmed. Hostile-based bipartite containment control of nonlinear fractional multi-agent systems with input delays: a signed graph approach under disturbance and switching networks[J]. AIMS Mathematics, 2024, 9(5): 12678-12699. doi: 10.3934/math.2024620

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Abstract

This article addresses the hostile-based bipartite containment control of nonlinear fractional multi-agent systems (FMASs) with input delays. Several fundamental algebraic criteria have been offered by the use of signed graph theory. To make the controller design more realistic, we assumed that the controller was under some disturbance. For the analysis of bipartite containment control, we used a fixed and switching signed network. The commonly used Lyapunov function approach and the Razumikhin technique were used. The use of these techniques can conquer the challenge brought on by switching, temporal delays, and fractional mathematics. To better elucidate the theoretical results, two examples are provided.

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