Leader-following consensus problem of multi-agent networks based on homogeneous polynomial Lyapunov functions

Leader-following consensus problem of multi-agent networks not only with switching topology but also with an active and incompletely measured leader is investigated. A criterion described by bilinear matrix inequalities is obtained based on the construction of homogeneous polynomial Lyapunov functions (HPLFs). A neighbor-based local controller and a neighbor-based state-estimation rule are designed to guarantee that: (i) each agent can follow the leader if the (acceleration) input of the active leader is known; and (ii) the tracking error is estimated if the input of the leader is unknown. Simulation results demonstrate that the larger control gain margin can be obtained by using HPLFs.