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

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.