Formation-containment control of second-order multi-agent systems with time delays

Formation‐Containment Control of Second‐Order Multiagent Systems via Intermittent Communication

“…Definition 1 (see [23][24][25][26]). The multiagent system (1) is said to achieve the desired formation-containment asymptotically, if…”

“…holds with ∈ [ , + ), where and are defined in condition ( ) of Theorem 8. In (24), and are the minimum control time and the maximum communication loss time, respectively. Meanwhile, we obtain from (23) that ( ) ≤ (0) e − 1 ( 0 + 1 +...+ )+ 2 ( 0 + 1 +...+ −1 + − − ) ≤ (0) e − 1 ( +1) + 2 ( +1) (25) holds with ∈ [ + , +1 ).…”

“…Zheng et al [23] studied the formationcontainment control problem of second-order multiagent systems with only sampled position data, and got sufficient formation-containment conditions based on algebraic graph theory and matrix theory. In addition, Xia et al [24] proposed the formation-containment control algorithms for secondorder multiagent systems under time-varying delays, and two delay-dependent convergence conditions were obtained for the leaders and followers, respectively, based on Lyapunov-Krasovskii functional. Moreover, Dong et al [25] analyzed the formation-containment problem of a high-order linear multiagent system with identical time-invariant delay and the convergence conditions were gained in the form of linear matrix inequalities.…”