Observer design for a class of nonlinear descriptor systems

This paper considers the problem of observer design for a class of nonlinear descriptor systems whose nonlinear terms are time-varying and satisfy a quadratic inequality. The error system is firstly represented by a Lur´e descriptor system (LDS). Then, motivated by the basic idea of absolute stability theory, both types of full-order and reduced-order observers are constructed by a unified approach. The proposed observers guarantee exponential convergence of the state estimation error to zero. Finally, the design methods are reduced to a linear matrix inequality problem and illustrated by an example.