Event-based integral sliding mode control for leader-follower consensus with perturbed agent dynamics

This manuscript proposes the design of an event-triggered integral sliding mode (ET-ISM)-based distributed controller for multi-agent systems (MASs) to achieve consensus between the leader and followers. Specifically, we consider the MASs, having multi-input-multi-output (MIMO) linear dynamics with unknown bounded perturbations. The information flow in the network is modelled by the directed graph. The design of the continuous-time integral sliding mode (ISM) controller is discussed first, followed by an ET-ISM strategy using a novel triggering rule to avoid periodic communication between the leader and agents. Unlike the earlier works, our proposed method uses an event function entirely devoid of non-differentiable terms to define the triggering condition. The stability of robust closed-loop dynamics of the network is guaranteed using Lyapunov stability theory, and the existence of practical sliding motion (PSM) is established by calculating the band for PSM as well as the band of convergence of the disagreement vector. The Zeno-free behaviour of the closed-loop system is also ensured to show that the sampling is well-behaved means the triggering approach generates a finite number of events. Finally, we take up a numerical example to discuss the design process of the proposed controller and present the simulation results along with a detailed analysis.