ON STABILITY OF COMMENSURATE FRACTIONAL ORDER SYSTEMS

This paper proposes a new proof of the Matignon's stability theorem. This theorem is the starting point of numerous results in the field of fractional order systems. However, in the original work, its proof is limited to a fractional order nu such that 0 < nu < 1. Moreover, it relies on Caputo's definition for fractional differentiation and the study of system trajectories for non-null initial conditions which is now questionable in regard of recent works. The new proof proposed here is based on a closed loop realization and the application of the Nyquist theorem. It does not rely on a peculiar definition of fractional differentiation and is valid for orders. such that 1 < nu < 2.