Information topology-independent consensus criteria for second-order systems under directed graph

In this paper, consensus seeking of second-order systems without leaders is investigated under possibly switching directed graphs. Two consensus algorithms using different cooperative schemes are proposed and some information topology-independent criteria are obtained. For the first one, an eigenvalue-based analysis is taken to attain a sufficient and necessary condition for consensus seeking under fixed directed graph. For the second one, consensus can be achieved as long as the union of the switching graphs has a directed spanning tree frequently enough. Convergence analysis is presented, which is facilitated by an equivalent model transformation into a cascaded system. A novel sufficient and necessary condition for consensus seeking under switching undirected graph is also obtained using the same strategy. Moreover, robustness of both the algorithms to time-delays is studied under fixed directed graph. Illustrative examples are also provided to show the effectiveness of the theoretical results.