Exploiting structure in piecewise affine identification of LFT systems

Linear fractional transformations (LFTs) represent a suitable framework for describing interconnections of linear and nonlinear components. This paper addresses the use of prior knowledge about the interconnection structure for the identification of such LFT systems from input-output data. An iterative algorithm is implemented, which alternates the identification of the linear and the nonlinear components, while estimating the unknown internal signals. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine (PWA) identification techniques are employed for modelling the nonlinearity. A numerical example analyzes the benefits of the structure-exploiting identification algorithm compared to applying black-box PWA identification techniques to the overall system.