Consensus analysis of continuous‐time second‐order multi‐agent systems with nonuniform time‐delays and switching topologies

In this study, consensus problems for second‐order multi‐agent systems with nonuniform and switching topologies are investigated. Each agent has a self‐delay, and each delay is independent of the others. As a measure of the disagreement dynamics, a class of positive semi‐definiteLyapunov–Krasovskii functions are introduced. Using algebraic graph theory and theseLyapunov–Krasovskii functions, sufficient conditions are derived by contradiction under which all agents asymptotically reach consensus. Finally, the effectiveness of the obtained theoretical results is demonstrated through numerical simulations.