Identification of linear systems: A graph point of view

This paper presents a methodology for model identification of SISO discrete-time linear systems. The approach relies on standard spectral estimation techniques which are then applied to the identification of a symbol for the graph. More specifically, the power spectrum of the stochastic process, which consists of both the inputs and the outputs of a given plant, is estimated and a symbol for the plant is identified as the inner part of a left canonical spectral factor of the spectrum. Bounds, in the L¿ sense, on the uncertainty in estimating power spectra are related to the error in identifying the plant which is measured in the L2-gap and the v-gap.