Estimating linear time-invariant models of nonlinear time-varying systems

The standard machinery for system identification of linear time-invariant ( LTI) models delivers a nominal model and a confidence (uncertainty) region around it, based on (second order moment) residual analysis and covariance estimation. In most cases this gives an uncertainty region that tends to ze ro as more and more data become available, even if the true system is nonli near and/or time-varying. In this paper, the reasons for this are displayed , and a characterization of the limit LTI model is gh,en under quite genera l conditions. Various ways are discussed, and tested, to obtain a more real istic limiting model, with uncertainty. These should reflect the distance t o the true possibly nonlinear, time-varying system, and also form a reliabl e basis for robust LTI control design.