Identification of stabilizable systems: closed-loop approximation

Abstract

Approximate modelling and identification of linear shift-invariant, possibly unstable, discrete-time systems, or plants, is studied in a framework compatible with the so-called robust stability concept for feedback systems. This unified framework is based on approximate modelling of the plant in the gap and graph metrics which is achieved here through approximation of certain closed-loop transfer functions by finite-dimensional systems. Properties of this approximate inverse modelling approach are studied and concrete rate of approximation results are given. Furthermore, a consistency result in the gap and graph metrics is given for a certain experimental estimate of the plant constructed from closed-loop input -output data in a stationary noise set-up under mild conditions on the unknown plant.