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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 $$C_d(s)\underset={}\to\Delta C_0((1+ s/\omega_b)/(1+ s/\omega_h))^d,$$ 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.

93B15Realizability of systems from input-output data
93C80Frequency-response methods
93C95Applications of control theory
Full Text: DOI
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[9] Raynaud, H. -F.; Zergaı\ddot{}noh, A.: State-space representation of fractional linear filters. Proceedings of the fourth ECC (1997)