Fractional-order models can describe atypical and nonlinear dynamic behaviors more flexibly than integer-order systems. This article investigates the consensus problem of positive fractional-order multi-agent systems over directed graphs using a distributed observer-based approach. First, a distributed observer is used to estimate the agents’ states, offering larger design flexibility than the classical Luenberger observer. Second, sufficient and necessary conditions for the positive consensus of fractional-order multi-agent systems are established based on positive system theory. As these conditions involve Laplacian matrix information, they are further optimized to sufficient conditions expressed as Riccati-type inequalities by considering the number of nodes in the directed graphs. A semidefinite programming algorithm for achieving consensus in observer-based positive fractional-order multi-agent systems is presented by solving the algebraic Riccati inequalities. Finally, the validity of the results is confirmed through a numerical simulation.
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