Stability and L8-Gain of Positive Fractional-Order Singular Systems With Time-Varying Delays

This brief investigates the stability and L-8-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-8-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.

Automated summary

This paper investigates the stability and L-8-gain of positive fractional-order singular systems with time-varying delays. An equivalent auxiliary system is developed to avoid singularity problem, and a criterion ensuring the positivity of delayed systems is established. The asymptotic stability and L-8-gain of systems are analyzed using the positivity and monotonicity of system solutions.