Nonlinear filtering for the linear fractional transformation model

In gain-scheduling control the linear fractional transformation (LFT) model is applied extensively to describe nonlinear plants. The equivalent representation of the nonlinear state space model by a linear model and a simple nonlinear feedback connection using the LFT is very efficient. Moreover, the existence of the model for any smooth nonlinear mapping makes the LFT amenable to the most general class of nonlinear systems. In this paper, we propose Bayesian filtering for this model and based on an approximation confined to the feedback loop only give a closed form solution to Bayes recursion. We demonstrate through simulations that the proposed filter works better than conventional approximation methods.