Multivariable Identification of Continuous-Time Fractional System

This paper presents two subspace-based methods, from the MOESP (MIMO output-error state space) family, for state-space identification of continuous-time fractional commensurate models from sampled input-output data. The methodology used in this paper involves a continuous-time fractional operator allowing to reformulate the problem so that the state-space matrices can be estimated with conventional discrete-time subspace techniques based on QR and singular value decompositions. The first method is a deterministic one whereas the second approach takes place in a stochastic context. The performance of both methods is demonstrated using Monte Carlo simulations at various signal-to-noise ratios. The deterministic method leads, as expected, to biased estimates. This bias is removed in the stochastic method by the use of an instrumental variable. As compared to rational systems, the commensurate differentiation order must be estimated besides the state-space matrices which is done using nonlinear programming. This is the first work developed for multi-input multi-output system identification using fractional models.