Robust Containment Control of Uncertain Multi-Agent Systems With Time-Delay and Heterogeneous Lipschitz Nonlinearity

This paper investigates the robust containment control problem of multiagent systems with heterogeneous uncertainty and nonlinearity while the nonlinear parts have to satisfy the Lipschitz condition. In this paper, both input time-delay and data transmission time-delay between the agents are considered simultaneously and communication topology of the multiagent systems may switch in the steady-state condition. Under the mentioned conditions, the objective of this paper is to make all the followers’ states converge to the convex hull shaped by the leaders’ states with an expected exponential rate. To this end, an appropriate smooth protocol is proposed. Then, a Lyapunov–Krasovskii functional composed of five terms is proposed and the stability condition is denoted by two linear matrix inequalities (LMIs). In addition to the stability assurance, solving the LMIs would obtain the suitable gains for the protocol. Finally, some numerical simulations are given to verify the theoretical analysis.