Jensen integral inequality approach to stability analysis of continuous-time systems with time-varying delay

The problem of stability analysis for continuous-time systems with time-varying delay is studied. 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, and this upper bound is allowed to be 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. Numerical examples are given to illustrate the effectiveness of the proposed methods.