<p>This paper investigates the consensus of positive fractional-order multiagent systems with sector input nonlinearities over directed graphs containing at least one spanning tree. Firstly, an observer-based protocol for positive consensus is proposed, offering greater design flexibility than the Luenberger observer-based protocol, while accounting for both input nonlinearities and positive constraints. Secondly, sufficient conditions for positive consensus are constructed using the nonzero eigenvalues of the Laplacian matrix. Since these conditions involve Laplacian matrix information, we further optimize them into sufficient conditions in terms of linear matrix inequalities (LMI) by utilizing the number of nodes in directed graphs. These conditions, using an improved positive definite Lyapunov function, are less conservative. Then the feedback matrix and the gain matrix are obtained by solving the LMI. Finally, the validity of the obtained results is verified through two numerical simulation experiments.</p>