Observer Design For One-Sided Lipschitz Nonlinear Systems

The investigation of the observer design for nonlinear systems has been brought to the attention of researchers. Researchers put forward many design methods, such as the extended Kalman filter, coordinate transform, Lyapunov-like methodology. This paper mainly deals with observer design for one-sided Lipschitz nonlinear systems based on Lyapunov theory and linear matrix inequality method. The main research contents are as follows:Firstly, a functional observer design for one-sided Lipschitz continuous nonlinear systems is dealt with. The sufficient conditions for gain matrices of a functional observer are obtained based on linear matrix inequalities. Then a design method for gain matrices of the functional observer is presented. Through a simulation example, it is illustrated that the proposed approach not only can estimate the states of the system but also make the observer errors converge to zero quick.Secondly, a functional observer design for one-sided Lipschitz discrete-time nonlinear systems is dealt with. Using Lyapunov theory, Schur Lemma and linear matrix inequalities, the sufficient conditions ensuring asymptotic stability of the functional observer is acquired, and the design method for gain matrices of the functional observer is derived. Simulation results show that the proposed approach makes the observer errors converge to zero quick.Thirdly, a full-order observer design for one-sided Lipschitz time-delay nonlinear systems is investigated. By constructing a Lyapunov-Krasovskii functional and using linear matrix inequalities, sufficient conditions for the existence of the state observer gain matrix and its design method are obtained. Simulation results show that the proposed observer can asymptotically track the states of the system.