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State-space representation for fractional order controllers. (English) Zbl 0964.93024
The authors’ abstract reads as follows:
“This article proposes an infinite-dimensional state-space realization for linear filters with transfer function \[ C_d(s)\underset={}\Delta C_0((1+ s/\omega_b)/(1+ s/\omega_h))^d, \] where \(0< \omega_b< \omega_h\) and \(0< d< 1\). This exponentially stable representation is derived from the Taylor expansion at zero of the function \((1- z)^d\), and is made up of an infinite number of first-order ordinary differential equations. Finite-dimensional approximations obtained by truncating this representation are shown to converge towards \(C_d\) in \(H_\infty\). An example of feedback loop incorporating this approximation of \(C_d\) (car suspension) is presented, for which robustness of closed-loop resonance and step response overshoot vis-à-vis a variation in the vehicle mass is achieved.”
This interesting paper finds its motivation in and is geared towards application to a real-world problem.
It is partly a marriage between an idea that dates back to Bode and modern infinite-dimensional systems theory as described and developed by Curtain and Zwart.

MSC:
93B15 Realizations from input-output data
93C80 Frequency-response methods in control theory
93C95 Application models in control theory
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References:
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