Coprime factorizations and stability of fractional differential systems

Stabilization of fractional exponential systems including delays

“…The next results extend the corresponding result of [1,2,3]. They are given without proof as this goes as in [3]. We will just give some hints to the reader.…”

“…Reference [9] and [3] consider transfer functions with polynomials and exponentials in fractional powers of s (reference [9] considering the particular case of the heat equation) as reference [8] and [2] analyze transfer functions with polynomials in fractional powers of s and delay terms (reference [7] considering the particular case of transfer functions of the type G(s) = aa a. 6 .…”

Performance Limitations of Non-Laminated Magnetic Suspension Systems

“…This conjecture was proven by Bonnet and Partington in 2000 [23]. A useful restatement of this result was provided by Zhu [24].…”

“…4. The result (23) shows that as the sensitivity over the frequency band is reduced (i.e., smaller ), the peak in sensitivity over the frequency range must increase no matter what stabilizing controller is employed. Furthermore, the sensitivity peak must also be amplified if the frequency range of sensitivity reduction is enlarged.…”

“…Suppose from a design standpoint that a target value of peak sensitivity is prescribed, which we will denote by (23) Combining (19), (21) and (22), it is straightforward to demonstrate that (24) where is the change in the log sensitivity desired from the attenuation band to the peak, i.e.,…”