Stabilization of linear time-varying descriptor systems: A linear matrix differential inequality approach

This paper considers stabilization of linear time-varying descriptor systems with continuous and bounded coefficient matrices. First, a necessary and sufficient condition for exponential stability is presented as solvability of a linear matrix differential inequality. Then, the stability condition is utilized to derive a feedback control law for stabilization of the descriptor system. The proposed feedback gain extracts the dynamic component of the descriptor variable. A numerical example is presented.