Analysis, Modeling, and Stability of Fractional Order Differential System: The Infinite State Approach

Modelling of FDEs and FDSs based on fractional integrators represents the generalization of integer order system theory to fractional systems, with important differences due to the specificities of fractional calculus. Fractional integration is performed using two equivalent techniques: frequency synthesis and a modal distributed approach. This modelling technique provides immediate solutions to different initialization problems: fractional derivatives and FDEs/FDSs. Definition of fractional integrator energy allows FDE stability analysis using Lyapunov technique.