Stability and L∞-Gain of Positive Fractional-Order Singular Systems With Time-Varying Delays

This brief investigates the stability and
$L_{\infty }$
-gain of positive fractional-order singular systems (FOSSs) with time-varying delays. Based on the Drazin inverse of singular matrices, an equivalent auxiliary system is developed to avoid the singularity problem, and a sufficient and necessary criterion ensuring the positivity of delayed FOSSs is established. Furthermore, the asymptotic stability and
$L_{\infty }$
-gain of FOSSs are analyzed using the positivity and monotonicity of system solutions instead of the fractional Lyapunov stability theorem. Finally, a simulation experiment utilizing electrical circuit system is carried out to justify the rationality of the results.