Research on Consistency of Delayed Multi-agent System Based on Markov Switching Topology

The first-order multi-agent system with Markov switching topology in continuous time is studied, and the average consistency problem under time delay is simulated. Solve the time delay caused by limited time information processing, physical limitations in the communication channel, and actuator response. Solve the problem of agent failures leading to changes in the group communication topology. This paper constructs a continuous-time multi-agent control protocol graph theory topology graph model. Using graph theory and orthogonal transformation methods, the average consistency problem of the system is transformed into a stability problem. Then use the definition of Lyapunov stability to select an appropriate symmetric matrix. And verification system based on stable conditions linear matrix inequality (LMI). Finally, the fixed topology and Markov switching topology of six agents are simulated, and the results are compared to verify the effectiveness of the method.