Practical consensus for heterogeneous linear time-varying multi-agent systems

This paper studies practical consensus (PC) problem for linear multi-agent systems (MAS) under a fixed, connected, and undirected communication network. PC means that the difference between any two agents remains in an arbitrarily chosen neighborhood of the origin after some time by using a suitable control law. All the agents, which are heterogeneous first-order linear time-varying (LTV) systems, can collect only relative state information from their neighborhoods. According to the assumptions of MAS, we divide the problem into two cases; one is a class of homogeneous LTV MAS with heterogeneous disturbances where the difference between any two disturbances is bounded, and the other is a class of heterogeneous LTV MAS with heterogeneous bounded disturbances. Finally, we show that PC for each case is always achieved if the control gain is sufficiently large.