Positivity and Reachability of Fractional Electrical Circuits

Abstract: Conditions for the positivity of fractional linear electrical circuits composed of resistors, coils, condensators and voltage (current) sources are established. It is shown that: 1) the fractional electrical circuit composed of resistors, coils and voltage source is positive for any values of their resistances, inductances and source voltages if and only if the number of coils is less or equal to the number of its linearly independent meshes, 2) the fractional electrical circuit is not positive for any values of its resistances, capacitances and source voltages if each its branch contains resistor, capacitor and voltage source, It is also shown that the fractional positive electrical circuits of R, C, e type are reachable if and only if the conductances between their nodes are zero and the fractional positive electrical circuits of R, L, e type are reachable if and only if the resistances belonging to two meshes are zero.

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