Algebraic conditions for monotonicity of magnitude-frequency responses in all-pole fractional order systems

This study deals with the investigation of the magnitude-frequency responses of all-pole fractional order systems in the viewpoint of extrema existence in these responses. In this investigation, a sufficient algebraic condition, two necessary algebraic conditions, and a necessary and sufficient algebraic condition are obtained to guarantee the non-existence of extrema in the magnitude-frequency response of all-pole fractional order systems. Some examples are presented to show the effectiveness of the results of the paper.