NISC Center would like to congratulate Dr. Ahmed G. Radwan for his accepted Journal Papers in 2016, Which is published in the Journal of Circuit Theory and Application
- Mourad S. Semary, Ahmed G. Radwan, Hany N. Hassan, “Fundamentals of Fractional-Order LTI Circuits and Systems: Number of Poles, Stability, Time and Frequency Responses,” International Journal of Circuit Theory and Application, in press 2016
This paper investigates some basic concepts of fractional-order linear time invariant systems related to their physical and non-physical transfer functions, poles, stability, time domain, frequency domain, and their relationships for different fractional-order differential equations. The analytical formula that calculates the number of poles in physical and non-physical s-plane for different orders is achieved and verified using many practical examples. The stability contour versus the number of poles in the physical s-plane for different fractional-order systems is discussed in addition to the effect of the non-physical poles on the steady state responses. Moreover, time domain responses based on Mittag-Leffler functions for both physical and non-physical transfer functions are discussed for different cases, which confirm the stability analysis. Many fractional-order linear time invariant systems based on fractional-order differential equations have been discussed numerically in both time and frequency domains to validate the previous fundamentals. Copyright © 2016 John Wiley & Sons, Ltd.