Observer Deisgn For Nonlinear System: Based On Quasi-one-sided Lipschitz Condition

Recently, the non-linear observer design question is one of the research issuepaid much attention by many scholars. That researches are made successful andmost of them are aimed at Lipschitz non-linear system state design. Studies haveshown that use Lipschitz only to design non-linear-system observer asymptotic sta-bility can not be achieved.In this paper, the observer design for the class of quasi-one-sided Lipschitz non-linear systems is investigated. Based on the quasi-one-sided Lipschitz condition, wepropose sufcient conditions of the existence of the observers for the class of nonlin-ear systems, these conditions are complements of those based on Lipschitz conditionin literature at least, and some of these conditions are less conservative than thosein literature. This paper shows that the quasi-one-sided Lipschitz constant matrixand the one-sided Lipschitz constant matrix are superior to the one-sided Lipschitzconstant and Lipschitz constant for observer design of a large number of nonlinearsystems. It should be noticed that some of the present results are directly appli-cable to not only the important class of the Lipschitz nonlinear systems but alsothe quasi-one-sided Lipschitz nonlinear systems which are not the usual Lipschitznonlinear systems. Some examples are given to illustrate the proposed approach.