Reduced-order observer design for systems with non-monotonic nonlinearities

The problem of constructing globally convergent, reduced-order observers for nonlinear systems is addressed. Current results on nonlinear observer design require that the nonlinearities appearing in the system equations are either linear functions of the unmeasured states or monotonic functions of a linear combination of the states. In this paper we relax these two assumptions by allowing for a wider class of nonlinearities to appear in the system equations. The proposed approach is demonstrated on a simple example and on the well-known "ball and beam" mechanical system.