State observation for systems with linear state dynamics and polynomial output

This paper investigates the problem of asymptotic state reconstruction for a class of continuous-time systems characterized by linear input-state dynamics and polynomial state-output function. It is shown that the dynamics of systems in this class can be embedded into the dynamics of systems of higher dimension, with time-varying linear state dynamics and linear state-output map. An asymptotic state observer for the original system is presented, whose design is based on the equations of the extended system. The observer gain is computed on-line by solving a Riccati differential equation. The interest in this observer is in its capability of state reconstruction also in cases in which the original system is not drift-observable (observable for zero input) nor uniformly observable (observable for any input).