Delay-range-dependent and rate-range-dependent stability criteria for linear systems with time-varying delays

The issue of the stability of linear systems with time-varying delays is considered in this paper. The time-delay considered in this paper belongs to a given interval and its derivative also belongs to a given interval. By constructing a new type of Lyapunov functional where some triple-integral terms are contained and the information of the lower bound on the delay is considered sufficiently, new stability criteria are derived in terms of linear matrix inequality without introducing any free-weighting matrices. The criteria are both delay-range-dependent and rate-range-dependent. Numerical examples are given to illustrate the effectiveness of the proposed method.