An exponential observer for discrete-time systems with bilinear drift and rational output functions

This paper presents an observer with exponential error decay for systems described by bilinear input-state dynamics and output functions that are ratios of polynomials in the state. It is shown that such kind of systems can be immersed into systems of higher dimension, with time-varying linear state dynamics and linear output map. The observer here presented is derived exploiting the structure of the extended system. Conditions of global exponential convergence are given and discussed. Computer simulations demonstrate good behavior of the observer, even in the presence of disturbances on the state and output equations.