access icon free 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.

Inspec keywords: frequency response; pole assignment; differential algebraic equations

Other keywords: extrema nonexistence; necessary and sufficient algebraic condition; magnitude frequency response monotonicity; all-pole fractional order system

Subjects: Control system analysis and synthesis methods; Differential equations (numerical analysis)

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