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 a satisfies 0 < alpha < 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.