Distributed <i>H</i>_∞ and <i>H</i>₂ Time-Varying Formation Tracking Control for Linear Multi-Agent Systems with Directed Topologies

In this paper, the <i>H</i>_∞ and <i>H</i>₂ time-varying formation tracking problems for multi-agent systems with directed topologies in the presence of external disturbances are investigated. The followers need to achieve the desired time-varying formation during movement and simultaneously track the state trajectory generated by the leader. First, a distributed consensus protocol based on the local state information of neighbors of the agents for solving <i>H</i>_∞ and <i>H</i>₂ time-varying formation tracking problems are proposed without utilizing global information about the entire agents. The conditions to achieve <i>H</i>_∞ and <i>H</i>₂ time-varying formation tracking in the presence of external disturbances are suggested respectively. Then, to determine the parameters of the designed protocol which satisfy suitable conditions, algorithms for <i>H</i>_∞ and <i>H</i>₂ time-varying formation tracking in the form of pseudo-code are presented, respectively. Furthermore, the proofs of the proposed theorems are derived by utilizing algebraic graph theory and Lyapunov analysis theory tools to demonstrate the closed-loop stability of the system in the presence of external disturbances. Finally, the usefulness and effectiveness of the approaches proposed are demonstrated by numerical simulation examples.