Fractional systems with commensurate orders inherit the monotonicity of magnitude-frequency response from their integer-order counterparts

It has been previously revealed that the stability and the monotonicity of step response in an integer-order LTI system are two specifications, which are preserved in its fractional counterparts possessing commensurate orders between zero and one. In this paper, it is shown that the monotonicity of magnitude-frequency is another specification which is inherited from integer-order systems to their commensurate order counterparts. This finding completes the trilogy of stability, extrema-freeness of the step response, and monotonicity of magnitude-frequency, as the specifications whose holding in integer-order systems yields in meeting them in their fractional-order counterparts with commensurate orders in the range (0,1). The obtained analytical result is confirmed by some examples on frequency-domain analysis of fractional-order systems.