On the identification of bilinear systems from operating records†

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Abstract
In this paper the identification of a non-linear system when the input-output record is available is considered. The system discussed is an open-loop system. It is assumed that the unobservable output x(t) at time t and the observable input {w(.s), s≤t} are related by a bilinear model. It is further assumed that only a contaminated version of the output is observed, i.e. y(t) whore, for each t, y(t) =x(t) + z(;t) and x(t) and z(t) are mutually independent. The identification of the system is considered in the following cases ; (i) where the external noise z(t) is a gaussian white noise, and (ii) where z(t) is a gaussian stationary time series satisfying an autoregressive moving average (ARMA) model of order (g, j). The estimation procedures are illustrated with examples.

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