Observer design for non-linear systems based on a generalised Lipschitz condition

The stability-sufficient condition in designing an observer for non-linear Lipschitz systems is extended such that it does not neglect the structure of given non-linearity and can be less conservative in applying to many non-linear systems. A design procedure based on full control problem is then presented to satisfy the extended condition by means of a constant observer gain. Finally, simulation examples are given to exhibit the effectiveness of the proposed condition and design procedure in dealing with some large Lipschitz non-linearities.