On the Consistency of Certain Identification Methods for Linear Parameter Varying Systems

Abstract: The consistency of identification methods for input-output models of Linear Parameter Varying systems is considered. In order to perform a consistency analysis the applicability of ergodicity is required, which is not obvious with these types of nonstationary systems. It is therefore shown that, when the scheduling parameter satisfies certain conditions, an ergodicity-type result can be applied to the signals considered. An analysis is then carried out for two cases: that of noise-free measurements of the scheduling parameter, and then the more realistic case of noisy scheduling parameter measurements. The latter is shown to be an errorsin-variables type problem. Since the least squares technique does not give consistent estimates, the instrumental variables method is proposed to achieve this property. The analysis carried out is reinforced by simulation results.