Design of observers for systems with rational output function

This note presents an approach for the design of asymptotic state observers for systems characterized by output functions that are ratios of polynomials in the state. The case of linear and bilinear input-state dynamics is considered, and conditions for exponential error decay are provided. The first step towards the construction of the observer is to show that the dynamics of a system in the considered class can be embedded into the dynamics of a system of higher dimension, with time-varying linear state dynamics and linear output map. The construction of the observer here proposed exploits the structure of the extended system. The solution of a Riccati differential equation provides the observer gain.