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Identication of Linear Parameter Varying Mo dels Bassam Bamieh Laura Giarre Bassam Bamieh is with the Department of Mechanical and Environmental Engineering, University of Califor- nia, Santa Barbara, CA 93106, USA, Phone: (805) 893 4490 , email:bamieh@engineering.ucsb.edu His Research is supp orted by NSF under CAREER award ECS-96-24152, and AFOSR-PRET 442530-25380 Laura Giarre is with the Dipartimento di Ingegneria Automatica e Informatica, Universita di Palermo, viale Delle Scienze, 90128 Palermo, Italy. Phone: (091) 481119 , email: giarre@ias.unipa.it 1 Identication of Linear Parameter Varying Mo dels Abstract We consider identication of a certain class of discrete-time nonlinear systems known as Linear Parameter Varying (LPV) system. We assume that inputs, outputs and the scheduling parameters are directly measured, and a form of the functional dep endence of the system co eÆcients on the parameters is known. We show how this identication problem can b e reduced to a linear regression, and provide compact formulae for the corresp onding Least Mean Square and Recursive Least Square algorithms. We derive conditions on p ersistency of excitation in terms of the inputs and scheduling parameter tra jectories when the functional dep endence is of p olynomial typ e. These conditions have a natural p olynomial interp olation interpretation, and do not require the scheduling parameter tra jectories to vary slowly. This metho d is illustrated with a simulation examp