Exponential consensus of nonlinear multi-agent systems with fractional Brownian motions via sliding mode control

By utilizing sliding mode control, this paper explores the exponential consensus of nonlinear multi-agent systems (MAS) with time-varying delays, which are subject to system’s perturbations and constrained by fractional Brownian motion and semi-Markovian jumps. First, an integral sliding mode surface is constructed based on the multi-agent error system while taking into account time-varying delays and establishing a relationship with the mode of semi-Markovian jumps. To facilitate stability analysis, a Lyapunov–Krasovskii functional (LKF) with double integrals is developed. By employing the generalized Ito formula for fractional Brownian motion and linear matrix inequalities theory, the p−th moment exponential stability of the error system is established, which can guarantee that the multi-agent systems achieve a consensus with an exponential decay rate. Next, a sliding mode controller is designed, and the finite-time reachability of the proposed sliding surface is examined, ensuring system trajectories reach the sliding surface within a finite time despite disturbances. Finally, the theoretical results are validated through simulations on a distributed microgrid model and supported by numerical examples, demonstrating the effectiveness and applicability of the proposed method.