Abstract: Due to the delay is timevarying and ranges in an interval， the problem of stability for descriptor systems with a delay was investigated. A criterion guaranteeing regularity， free impulse and asymptotic stability were formulated in terms of four linear matrix inequalities. The delay interval was partitioned into two equal subintervals， for each of which， the coefficients of the integrals were enlarged by appropriate inequalities. The upper bound of the derivative of the LyapunovKrasovskii functional was expressed as an affine function with respect to some parameter. Two linear matrix inequalities were derived to guarantee the negativity of such derivative. Therefore， the convex combination method in the literature had been generalized. Theoretical analysis and an example showed the result obtained was less conservative than those of some existing ones.

Key words: timevarying delay, descriptor systems, stability, LyapunovKrasovskii functional, linear matrix inequalities