Design Finite-time Consensus Protocol for High-order Linear Multi-agent Systems: A Gain Scheduled Approach

This paper revisits the finite-time consensus problem for high-order linear multi-agent networks by using smooth state-feedback. By following a gain scheduled approach, this paper first presents finite-time consensus protocol with a state-independent parameter, which takes the time-varying solution of parametric Lyapunov equation to design control gain. Note that the state-independent parameter is selected based on the connectivity of topology, which is a piece of global information. To get rid of this dependence, a node-based adaptive parameter is further proposed to achieve fully distributed consensus. Through finite-time stability theory, both the prepared parameters, including state-independent and adaptive parameters, for control protocol make the agents achieve finite-time consensus. Particularly, a specific convergence time is given by following the concept of finite-time escaping function. Finally, we provide a practical simulation on finite-time formation problem of six satellites, demonstrating the validity of theoretical results.