Distributed consensus of multi-agent systems with fault in transmission of control input and time-varying delays

This paper discusses the distributed consensus problem of linear dynamical multi-agent systems with missing control input in some intervals and also delay. At first, assuming zero control input in some intervals and delay, the model of system in such conditions is formulated. Then, a distributed adaptive controller based on the relative states of neighboring agents is proposed. By constructing a set of switching Lyapunov–Krasovskii functional, a new delay-dependent exponential ultimately bounded consensus criterion with explicitly exponential convergence rate is established. Furthermore, the obtained condition will be extended to the multi-agent system, when a false signal is injected instead of the nominal control signal in some intervals. Finally, an illustrative example is solved to show the advantage of the proposed approach.