Interval Observer-Based Coordination Control for Discrete-Time Multi-Agent Systems

In this article, the coordination control problem of discrete-time multiagent systems (MASs) affected by uncertainties, namely unknown initial states and external disturbances, is considered. Inspired by the interval observer constructed by the single system, the definition of distributed interval observer for discrete-time MASs is given, in which the control protocol of each agent obtained by solving a modified algebraic Riccati equation depends on the bounded information of the interval observer connected to itself and its neighbors. By the cooperativity theory and Lyapunov stability theory, it is established that the distributed interval observer can not only access some information about MASs at any instant, that is, the upper and lower bounds of each component of the agent state, but also realize the cooperative behavior of MASs under some essential conditions involving network synchronization and the unstable eigenvalue of the system matrix. In addition, with the help of a new time-varying transformation matrix, the new interval observer is constructed to eliminate the non-negative constraint. Finally, two numerical simulations are provided to confirm the validity of the derived results.