Observers for one-sided Lipschitz non-linear systems

In this paper, observer design of a class of non-linear systems is considered. The one-sided Lipschitz condition is introduced to estimate the influence of non-linear vector functions on the observer. Based on the one-sided Lipschitz condition, sufficient conditions for the existence of observers of the class of non-linear systems are presented which are less conservative than the results based on Lipschitz condition in literature. When the linear part of non-linear systems is not stabilized by the observer gain matrix, a sufficient condition for the observer design is given which shows that a negative one-sided Lipschitz constant, which includes information of the non-linear part, is useful to design a non-linear observer.