Consensus tracking algorithms with directed network

This paper considers consensus tracking of multi-agent systems with general linear dynamics and a leader whose control input is nonzero and unavailable to any follower. Two tracking algorithms are designed for each follower. We prove that the followers can track the leader using both algorithms if the interaction graph among them is directed and there exists a directed path from the leader to each follower. For the first algorithm, each follower calculates the neighbors0 control inputs based on their states, then the stability condition is given based on the algebra Riccati inequality. The second algorithm utilizes neighbors0 states directly and the followers can track the leader with the aforementioned topology based on the algebra Riccati inequality. Simulations indicate the capabilities of the algorithms.