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 nonlinear 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.