AbstractWe consider identification of a certain class of discrete‐time nonlinear systems known as linear parameter varying system. We assume that inputs, outputs and the scheduling parameters are directly measured, and a form of the functional dependence of the system coefficients on the parameters is known. We show how this identification problem can be reduced to a linear regression, and provide compact formulae for the corresponding least mean square and recursive least‐squares algorithms. We derive conditions on persistency of excitation in terms of the inputs and scheduling parameter trajectories when the functional dependence is of polynomial type. These conditions have a natural polynomial interpolation interpretation, and do not require the scheduling parameter trajectories to vary slowly. This method is illustrated with a simulation example using two different parameter trajectories. Copyright © 2002 John Wiley & Sons, Ltd.