Distributed asynchronous consensus control of nonlinear multi-agent systems under directed switching topologies

This paper proposes a new Lyapunov function to study the distributed consensus problem for nonlinear multi-agent systems whose topologies are asynchronously switched with respect to observers. To be specific, we take into account the detection delay of topology switchings when designing the corresponding observers. The novelty of the design arises in the continuity of the Lyapunov function at the switching instants and in the discontinuity when the topology modes and the observer modes are matched. This property can possibly allow the value of the Lyapunov function to be non-increasing during the unmatched intervals, which reduces the conservativeness of topology switching signal in the sense that a more relaxed condition than state-of-the-art ones can be obtained. Moreover, a new Laplacian matrix is incorporated into our design to handle the dilemma that each agent can only receive the local neighboring information from the common neighbors before and after topology switchings. Hypersonic flight vehicles have been employed to verify the effectiveness of the theoretical findings.