Abstract: Output feedback stabilization is discussed for fractional-order uncertain systems, under two scenarios with fractional order 0<α<1 and 1≤α<2 respectively. Based on the output feedback controller designed, the condition of global stability is obtained using roots of characteristic equation and the Kronecker product of matrix. Finally, the condition of system stability is given in the form of Linear Matrix Inequality (LMI) by Schur complement lemma and singular value decomposition of matrix, which is easy to solve gain matrix.