A Drazin inverse approach to solvability, positivity, stability and P – M synchronization of singular fractional-order systems of arbitrary index

This paper studies a class of singular fractional-order systems using the Drazin inverse technique. In contrast to most existing works limited to index-one cases, the proposed approach applies to singular systems of arbitrary index. A decomposition result is established to reduce the original system to lower-dimensional subsystems, from which solvability conditions and an explicit solution representation are obtained. Positivity conditions are derived for both singular fractional systems with external functions and autonomous singular fractional systems. The asymptotic stability of the considered systems is then analyzed via spectral methods, and stability criteria for autonomous positive singular fractional systems are further established. As an application, a P–M synchronization scheme is developed for fractional singular systems with possibly different state dimensions. Numerical examples involving electrical circuit models are provided to illustrate the solvability, stability, and synchronization results.