Consensus of fractional‐order heterogeneous multi‐agent systems

This study is devoted to the consensus protocols design for a set of fractional‐order heterogeneous agents, which is composed of two kinds of agents differed by their dynamics and the fractional‐order α satisfies 0 < α < 2. Distributed state feedback consensus protocols are constructed for the two kinds of agents, respectively. Based on the Kronecker product technique and the fractional‐order stability theory, sufficient conditions are derived to ensure the consensus of heterogeneous multi‐agent systems in terms of linear matrix inequalities (LMIs). These can be solved numerically by LMI toolbox in Matlab. Finally, a simulation example is employed to validate the effectiveness of the theoretical results.