Fully distributed control for fixed-time synchronization of double-integrator-type multi-agent systems with time-varying delays

Fully distributed control protocol design problem for multiagent systems with double integrator dynamic on connected graphs is addressed in this content. Firstly, in order to deal with the time-varying delay, the prediction algorithm and the state transformation equation are introduced to obtain two new states. Secondly, a nonlinear gain sliding surface is designed so that both practical fixed-time control and improved convergence quality can be achieved. Lastly, using the Lyapunov method, strict stability proof for delayed double-integrator-type multi-agent system is given. Numerical simulation results are provided to verify the feasibility of our method.