H∞ Model Reduction for Fractional-Order Linear Systems

This paper focuses on the H-infinity model reduction problem of fractional-order linear systems with commensurate fractional order 0 < alpha < 1. Firstly, resorting to the H-infinity bounded real lemma, a design method based on the linear matrix inequalities is proposed to construct an asymptotically stable reduced-order model for the given stable fractional-order linear system, such that the H-infinity norm of the error between the transfer function of the reduced-order model and the transfer function of the given stable fractional-order system is less than the prescribed H-infinity performance. Secondly, by introducing a free-weighting matrix and congruent transformation, the system parameters of the reduced-order model are decoupled with the complex matrix variable and parameterized by another free-weighting matrix variable. Finally, one numerical example are given to illustrate the effectiveness of the proposed theoretical results.