Observer Design For A Class Of Uncertain Nonlinear Systems

Because of the complexity of nonlinear systems and nonlinear characteristics, itdoes not exist a general method of ordinary for observers design of nonlinear systems.So far, most of the existing research results are based on Lipschitz condition onthe problem of observers design for uncertain nonlinear systems. In this paper,byusing quasi-one-sided Lipschitz condition instead of the classical Lipschitz condition,the LMI approach of observers design for a class of uncertain nonlinear systemswith quasi-one-sided Lipschitz condition is given, and is applied to their robustH∞observers design. It is shown that unnecessarily positive-defnite (especially,negative defnite) quasi-one-sided Lipschitz constant matrix includes much usefulinformation and contributes to the asymptotical stability of the observers error. Thecriterion for the asymptotical stability of the observers error has less conservativethan those given in literature based on Lipschitz condition. It is still available evenif the parameters matrix of system and the parameters matrix of error system areunstable. Finally, the numerical example is given to illustrate the correctness of theapproach.