Reduced-order H∞ filtering for commensurate fractional-order systems

This paper is concerned with the reduced-order H_∞ filtering problem of commensurate fractional-order systems. Our goal is to construct a reduced-order filter in such a way that the filtering error is within a prescribed H_∞-norm error bound. Based on the bounded real lemma for commensurate fractional-order systems, a sufficient condition is established in terms of linear matrix inequalities (LMIs) under which the stability as well as the H_∞ performance of the filtering error system can be guaranteed. Moreover, by introducing a free real matrix variable, the desired filtering matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable, which facilitates the filter synthesis. Then, an iterative LMI algorithm is proposed to compute the filtering matrices accordingly. Finally, a numerical example is presented to show the effectiveness of the proposed algorithms.