Handling a Commensurate, Incommensurate, and Singular Fractional-Order Linear Time-Invariant System

From the perspective of the importance of the fractional-order linear time-invariant (FoLTI) system in plenty of applied science fields, such as control theory, signal processing, and communications, this work aims to provide certain generic solutions for commensurate and incommensurate cases of these systems in light of the Adomian decomposition method. Accordingly, we also generate another general solution of the singular FoLTI system with the use of the same methodology. Several more numerical examples are given to illustrate the core points of the perturbations of the considered singular FoLTI systems that can ultimately generate a variety of corresponding solutions.

Automated summary

This study aims to provide generic solutions for commensurate and incommensurate cases of fractional-order linear time-invariant (FoLTI) systems using the Adomian decomposition method. Additionally, a general solution for singular FoLTI systems is obtained using the same methodology. Numerical examples are provided to illustrate the core points of perturbations in these singular FoLTI systems, which can generate various corresponding solutions.