State estimation of unknown input polynomial systems: A sum of squares approach

In this paper, we address the problem of state estimating for a class of nonlinear systems that can be described by polynomial models subject to unknown inputs. The proposed observer is developed to guarantee the asymptotic convergence of the estimation error using the Lyapunov method and numerical tools. Sufficient design conditions are given in Sum Of Squares (SOS) formulation with equalities constraints for both continuous and discrete time cases. Thus, the given design conditions are numerically solved via the SOSTOOLS software and a semi definite program (SDP) solver. Finally, illustrative examples are given to provide the effectiveness of the proposed methodology.