Self-triggered consensus control for linear multi-agent systems with input saturation

In this paper, we study the consensus problem for a class of linear multi-agent systems (MASs) with consideration of input saturation under the self-triggered mechanism. In the context of discrete-time systems, a self-triggered strategy is developed to determine the time interval between the adjacent triggers. The triggering condition is designed by using the current sampled consensus error. Furthermore, the consensus control protocol is designed by means of a state feedback approach. It is shown that the considered multi-agent systems can reach consensus with the presented algorithm. Some sufficient conditions are proposed in the form of linear matrix inequalities (LMIs) to show the positively invariant property of the domain of attraction (DOA) . Moreover, some sufficient conditions of controller synthesis are provided to enlarge the volume of the DOA and obtain the control gain matrix. A numerical example is simulated to demonstrate the effectiveness of the theoretical analysis results.