Disturbance rejection for interconnected positive systems and its application to formation control of quadrotors

This study deals with disturbance rejection of interconnected positive (IP) systems by output feedback laws that are installed as an outer loop of the IP system. Since the IP system without disturbances has a first integral, which is a linear function of the state and takes a constant value along the trajectories, this study utilises this function as an index of detecting the disturbances. Then, dynamic and static disturbance rejection output feedback laws with the first integral are proposed, respectively. Although the pole assignment problem of the IP system with the static output feedback law is not solvable in general, this study reveals that the system matrix of the closed-loop system has a structure called rank-one updated matrices. This special structure implies that the simple eigenvalue zero of the original IP system moves to a stable one by the feedback law while the other stable eigenvalues never move. This study applies these feedback laws to formation control of quadrotors based on IP systems where the dynamics of a quadrotor are linearised to be positive and stable second-order subsystems by dual quaternion techniques. Numerical examples illustrate the quadrotors achieve a designed shape of formation against the disturbances.