H∞H∞ observers design for a class of nonlinear singular systems

The present paper is devoted to the H∞H∞ observer or filter design problem for a class of Lipschitz nonlinear singular systems. The approach is based on the parameterization of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given. The method also unifies the design for the full-order, reduced-order, minimal-order observers for continuous time systems. It can be seen that the obtained conditions when applied to linear systems are also necessary. A numerical example is given to show the applicability of our results.