Nonlinear observer design for a class of nonlinear systems with non-Lipschitz nonlinearities of the unmeasured states

A nonlinear observer is presented for a class of nonlinear systems with non-Lipchitz nonlinearities of the unmeasured states such as affine multiplicative nonlinearities term of the derivative of the measured output and monotonic nonlinearities of the unmeasured states. The resulting nonlinear estimation error system is represented as the feedback interconnection of a linear system and time-varying multivariable sector nonlinearity. The observer gain matrix is computed to satisfy a LMI and drive the estimation error to zero. The observer can be incorporated in output feedback using observer backstepping method in special forms.