Subspace method for continuous-time fractional system identification

Abstract: The aim of this paper is to develop a subspace method for state-space identification of continuous-time systems using fractional commensurate models. As compared to the classical state-space representation, the commensurate differentiation order must be estimated besides the state-space matrices. The latter are estimated with conventional subspace-based techniques using QR and singular value decompositions, whereas the commensurate order is estimated using nonlinear programming. This is the first method developed for multi-input multi-output system identification of fractional models. The performances are demonstrated by simulations at various signal-to-noise ratios assuming a known then an unknown commensurate order.