On the stability of linear systems with fractional-order elements


Linear integer-order circuits are a narrow subset of rational-order circuits which are in turn a subset of fractional-order. Here, we study the stability of circuits having one fractional element, two fractional elements of the same order or two fractional elements of different order. A general procedure for studying the stability of a system with many fractional elements is also given. It is worth noting that a fractional element is one whose impedance in the complex frequency s-domain is proportional to s? and ? is a positive or negative fractional-order. Different transformations and methods will be illustrated via examples. © 2007 Elsevier Ltd. All rights reserved.


Radwan A.G., Soliman A.M., Elwakil A.S., Sedeek A.


Complex frequencies; Different orders; S domains; Linear systems; System stability; Electric network analysis

Document Type



Chaos, Solitons and Fractals, Vol. 40, PP. 2317 to 2328, Doi: 10.1016/j.chaos.2007.10.033

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