Two equivalent lyapunov functionals on stability analysis for discrete-time systems with interval time-varying delays

Based on He and Zhang´s work in [18] and [19], this paper deals with the equivalence of two different Lyapunov functionals for discrete-time systems with interval time-varying time-delay. Although the Lyapunov functionals He and Zhang selected are different, we first proves they have equal effectiveness except the introducing of free-weighting matrices, then analyzes their computing burdens and conservatives, and this may be helpful for controllers design correspondingly.