Observer design for a class of nonlinear descriptor systems

The observer design problem for a class of nonlinear descriptor systems is considered. Nonlinear generalized proportional integral observers and nonlinear generalized proportional integral derivative observers are proposed. Using the differential mean value theorem, we transform the nonlinear error dynamics descriptor system into a linear parameter varying descriptor system. Then the stability of the error system is analyzed by a Lyapunov function, which shows that the errors are exponentially convergent. If the given linear matrix inequalities are feasible, all the gain matrices can be obtained. Compared with the existing observer design methods, the proposed methods offer more degrees of design freedom. As a result, a more comprehensive type of nonlinear descriptor systems can be designed and better transient performance and robustness against noise can be achieved. Finally, examples are given to illustrate the proposed methods.