Discrete double integrator consensus

A distributed double integrator discrete time consensus protocol is presented along with stability analysis. The protocol will achieve consensus when the communication topology contains at least a directed spanning tree. Average consensus is achieved when the communication topology is strongly connected and balanced, where average consensus for double integrator systems is discussed. For second order systems average consensus occurs when the information states tend toward the average of the current information states not their initial values. Lastly, perturbation to the consensus protocol is addressed. Using a designed perturbation input, an algorithm is presented that accurately tracks the center of a vehicle formation in a decentralized manner.