Nonlinear observers for a class of nonlinear descriptor systems

SUMMARY This paper considers a class of nonlinear descriptor systems whose nonlinear terms are time‐varying and satisfy a quadratic inequality. An nonlinear observer is constructed and the error system is represented by a Lur'e descriptor system (LDS). 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 method generalizes the existing ones for standard state‐space systems, and global convergence of the nonlinear observer is achieved without the usual global Lipschitz restriction. Furthermore, the stability criterion for the error system extends the existing ones for LDS in the sense that the involved interconnected nonlinearities are time‐varying and in unbounded sector. Finally, the design methods are reduced to a linear matrix inequality problem and illustrated by two numerical examples.