Closed-loop identification of unstable systems using noncausal FIR models

Motivated by the potential advantages of FIR model structures, the present paper considers the applicability of FIR models to closed-loop identification of open-loop-unstable plants. We show that FIR models can be used effectively for closed-loop identification of open-loop-unstable plants. The key insight in this regard is to realize that a noncausal FIR model can serve as a truncated Laurent expansion inside the annulus between the asymptotically stable pole of largest modulus and the unstable pole of smallest modulus. The key to identifying the noncausal plant model is to delay the measured output relative to the measured input. With this techniques, the identified FIR model is precisely a noncausal approximation of the unstable plant, that is, an approximation of the Laurent expansion of the plant inside the annulus of analyticity lying between the disk of stable poles and the punctured plane of unstable poles.