State observers for systems with sensors modeled by polynomials and rational functions

The problem of asymptotic state reconstruction of systems characterized by nonlinear state-output maps is investigated in this paper. The approach here presented is based on the approximation of output maps by means of polynomials or by ratios of polynomials, also named rational functions (RF). In previous papers the authors showed that when the input-state dynamics is bilinear and the output maps are RF's, the system can be immersed into a time-varying linear system of a larger dimension, denoted extended system, suitable for the observer construction. In this paper some issues on the observability property of the extended system are discussed and an alternative version of the observer is presented. Computer simulations on saturated sensor models demonstrate good behavior of the observer, even in the presence of state and output noises.