Output formation containment of time-delayed heterogeneous singular multi-agent systems with stochastic impulsive effects

Mhamed Benaissa; Esmail H. A. Al-Sabri; Maryam Iqbal; Walid Abdelfattah; Ghada A. Alsawah; Azmat Ullah Khan Niazi; Mhamed Benaissa; Esmail H. A. Al-Sabri; Maryam Iqbal; Walid Abdelfattah; Ghada A. Alsawah; Azmat Ullah Khan Niazi

doi:10.3934/math.2026482

AIMS Mathematics

2026, Volume 11, Issue 4: 11706-11730. doi: 10.3934/math.2026482

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Research article

Output formation containment of time-delayed heterogeneous singular multi-agent systems with stochastic impulsive effects

1.
Department of Chemical Engineering, University of Ha'il, Saudi Arabia
2.
Department of Mathematics, faculty of science, King Khalid University, Abha, Saudi Arabia
3.
Department of Mathematics and Computer, faculty of science, Ibb University, Yemen
4.
Department of Mathematics and Statistics, the University of Lahore, Sargodha Pakistan
5.
Humanities and Social Research Center, Northern Border University, Arar, Saudi Arabia
6.
Department of Industrial and Systems Engineering, College of Engineering, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 15 February 2026 Revised: 05 April 2026 Accepted: 21 April 2026 Published: 28 April 2026
MSC : 26A33, 34K37

This paper investigates the containment of output formation for heterogeneous singular multi-agent systems (MASs) subject to time delays and stochastic impulsive disturbances. The considered agents exhibit diverse dynamics, including descriptor-type tracking and algebraic systems, reflecting heterogeneity in state-space representations. Communication constraints are modeled via bounded state and input delays, while environmental uncertainties are captured through stochastic noise and impulsive effects occurring at arbitrary time instants. A distributed control protocol is proposed to achieve output formation containment, ensuring asymptotic convergence of follower outputs to a convex combination of leader outputs. The approach effectively addresses system singularities and uncertainties by employing a Lyapunov–Krasovskii functional combined with stochastic stability analysis. Sufficient conditions for mean-square admissibility and asymptotic convergence are derived. Numerical simulations validate the effectiveness and robustness of the proposed control strategy under varying delays and impulsive conditions.
- heterogeneous singular multi-agent systems,
- stochastic impulsive disturbances,
- formation containment,
- time delay
Citation: Mhamed Benaissa, Esmail H. A. Al-Sabri, Maryam Iqbal, Walid Abdelfattah, Ghada A. Alsawah, Azmat Ullah Khan Niazi. Output formation containment of time-delayed heterogeneous singular multi-agent systems with stochastic impulsive effects[J]. AIMS Mathematics, 2026, 11(4): 11706-11730. doi: 10.3934/math.2026482

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Abstract

This paper investigates the containment of output formation for heterogeneous singular multi-agent systems (MASs) subject to time delays and stochastic impulsive disturbances. The considered agents exhibit diverse dynamics, including descriptor-type tracking and algebraic systems, reflecting heterogeneity in state-space representations. Communication constraints are modeled via bounded state and input delays, while environmental uncertainties are captured through stochastic noise and impulsive effects occurring at arbitrary time instants. A distributed control protocol is proposed to achieve output formation containment, ensuring asymptotic convergence of follower outputs to a convex combination of leader outputs. The approach effectively addresses system singularities and uncertainties by employing a Lyapunov–Krasovskii functional combined with stochastic stability analysis. Sufficient conditions for mean-square admissibility and asymptotic convergence are derived. Numerical simulations validate the effectiveness and robustness of the proposed control strategy under varying delays and impulsive conditions.

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