A computing approach for delay margin of linear fractional-order retarded systems with commensurate time delays

This paper proposes a computing approach for the delay margin of fractional-order retarded systems with commensurate time delays. By the Orlando formula, a matrix constructed by the coefficients and commensurate fractional-order of the characteristic function is defined. By calculating the eigenvalues of this matrix, the existence conditions and computing approach are proposed. If the matrix has some positive real eigenvalues, a finite delay margin exists. If the matrix has no positive real eigenvalue, the delay margin is infinity and the system is stable, independent of the delay margin. Finally, a numerical example and simulation results are given to demonstrate the effectiveness of this approach.