Aas 13-771 a Linear-time-varying Approach for Exact Identification of Bilinear Discrete-time Systems by Interaction Matrices

Bilinear systems offer a promising approach for nonlinear control because a broad class of nonlinear problems can be reformulated in bilinear form. In this paper system identification is shown to be a technique to obtain such a bilinear approximation of a nonlinear system. Recent discrete-time bilinear model identification methods rely on Input-Output-to-State Representations. These IOSRs are exact only for a certain class of bilinear systems, and they are also limited by high dimensionality and explicit bounds on the input magnitude. This paper offers new IOSRs where the bilinear system is treated as a linear time-varying system through the use of specialized input signals. All the mentioned limitations are overcome by the new approach, leading to more accurate and less computationally demanding identification methods for bilinear discrete-time models, which are also shown via examples to be applicable to the identification of bilinear models approximating more general nonlinear systems.