Stable Nonlinear System Identification: Convexity, Model Class, and Consistency

Recently a new approach to black-box nonlinear system identification has been introduced which searches over a convex set of stable nonlinear models for the one which minimizes a convex upper bound of long-term simulation error. In this paper, we further study the properties of the proposed model set and identification algorithm and provide two theoretical results: (a) we show that the proposed model set includes all quadratically stable nonlinear systems, as well as some more complex systems; (b) we study the statistical consistency of the proposed identification method applied to a linear system with noisy measurements. It is shown a modification related to instrumental variables gives consistent parameter estimates.