New stability criteria for systems with time-varying delay

This paper studies the problem of stability for continuous-time systems with time-varying delay. By defining novel Lyapunov functionals and using the Jenson integral inequality, new delay-dependent stability conditions are obtained in terms of linear matrix inequalities. Unlike previous methods, the upper bound of the delay derivative is taken into consideration even if this upper bound is greater than or equal to 1. It is proved that the newly proposed criteria may introduce less conservatism than some existing ones. Meanwhile, the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved. A numerical example is given to illustrate the effectiveness of the proposed methods.