Stability of retarded time-delay systems: Extensively augmented lyapunov functional approach

The problem of stability of linear time-delay systems of retarded type is taken into consideration. A new extensively augmented Lyapunov-Krasovskii functional is introduced and some sufficient delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs). Utilization of any model transformation method or any kind of bounding for the cross terms are strictly avoided in the stability analysis. Moreover, in order to reduce the complexity of the solution of the LMI set, the proposed method does not also employ any relaxation such as the recently given free weighting matrix approach. A numerical example is illustrated to indicate the effectiveness of the proposed method.