Review of Stability Analyses of Formation Control with Time Delay

To research the stability of a formation control system with time delays systematically, two types of formalized descriptions of formation stability were presented. From the individual dynamic models, formation control strategies with time delays based on linear or non-linear feedback control and their corresponding mathematical models were reviewed. For different formation control strategies, specified formation missions and different time-delay cases, the main stability analysis methods for formation control systems were investigated, including the eigenvalue analysis method, the Lyapunov stability theory method, the Hamilton dissipation theory method and so on. Furthermore, the conclusions obtained by researchers using the above analysis methods were introduced. The advantages and disadvantages of these analysis methods for formation control with time delays were summarized, and the research tendency was described in the end.