Consensus for hybrid multi-agent systems with pulse-modulated protocols

We consider consensus in this paper for hybrid multi-agent systems (HMASs) consisting of continuous-time dynamic agents and discrete-time dynamic agents via designing pulse-modulated protocols. By assuming all the agents communicate with its neighbors only at some sampling instants, and the input of each continuous-time agent is determined by a pulse function, the consensus for first-order HMASs and second-order HMASs are addressed, respectively. According to the model transformation, stochastic matrix theory and the mathematical analysis technique, some sufficient criteria for consensus of these two types of HMASs are derived where it shows that the consensus in the considered HMASs can be achieved when the network structure, pulse function and sampling period respectively satisfy some suitable conditions. And, an algorithm is presented to evaluate the maximum allowable sampling period for achieving consensus. Finally, three numerical simulation examples are performed to validate the main theoretical results.