Abstract:  In order to solve the problem of the stability analysis of the linear descriptor fractional-order systems,
the continuous frequency distributed equivalent model and the indirect Lyapunov approach are applied in the
research of the linear descriptor fractional-order systems, an PD(Proportional-Derivative) controller is proposed
to normalize the descriptor fractional order system. A novel sufficient condition for asymptotic stability of the
descriptor fractional-order system with the order α(0<α<1) is presented. LMI(Linear Matrix Inequalities)
techniques and matrix’s SVD (Singular Value Decomposition) are used to obtain the results. A numerical
example is provided to demonstrate the effectiveness of the proposed methods.

Key words:  robust control, singular value decomposition(SVD), linear matrix inequalities(LMI), descriptor fractional-order system