Abstract: On the assumption that the delay is timevarying and ranges in an interval， the stability of linear systems with a delay was studied. Based on a LyapunovKrasovskii functional of quadratic type， a new stability criterion dependent on the delay range was proposed by employing the convex combination of integrals and Jensen’s integral inequality. Partitioning the delay range into segments， the coefficients of integral terms in the derivative of the LyapunovKrasovskii functional were enlarged by using appropriate inequalities for each segment. The conservatism of the convex combination method was reduced due to not using unified inequality for different segments. Theoretical analysis and numerical examples showed that the result obtained had less conservatism than that of some existing ones.

Key words: timevarying delay, stability, LyapunovKrasovskii functional, linear matrix inequalities, integral inequality