State estimation in nonlinear quadratic systems

The problem of the state estimation of nonlinear quadratic systems is addressed in this paper. Given an assigned polytopic region of the state space, which is enclosed into the domain of attraction of the zero equilibrium point, the main result consists of a sufficient condition for the existence of an observer which guarantees that the estimation error converges to zero, with an assigned rate, over such a prescribed region. The problem of the observer design is tackled in terms of a Linear Matrix Inequalities (LMIs) feasibility problem. Finally, the applicability of the proposed technique is discussed and illustrated through a numerical example.