Observer design for systems with an energy preserving nonlinearity, with application to fluid flow

In this paper observer design is considered for a class of non-linear systems whose non-linear part is energy preserving. Examples of such systems arise from considering finite dimensional approximations of fluid flows. A strategy to construct convergent observers for this class of non-linear system is presented. The approach has the advantage that it is possible, via convex programming, to prove whether the constructed observer converges, in contrast to several existing approaches to observer design for non-linear systems. Finally the method is used to produce a globally convergent observer for the Lorenz attractor.