Identi cation of Linear Parametrically Varying Systems

In this paper, we address the problem of identiication of linear parametrically varying systems, where the system coeecients are rational functions of the parameters. We obtain results for the case of one measurable varying parameter. Under the assumption of full state measurements, we show that this nonlinear identiication problem can be reduced to a set of n (dimension of state space) linear least squares problems. Further , we show that these recursions do estimate the parameters of the original model exactly under certain assumptions on the parameter variations. In the case of noisy state measurements we set up the problem as a set of n instrument variable recursions. Once again we demonstrate strong consistency of estimates. Simulations are presented to illustrate the results.