In this paper, we provide a bound of the continuous ARE solution in terms of a matrix associated with Lyapunov solutions. Based on the new matrix-type bound, we also consider various scalar bounds and compare them with existing bounds. The major advantage of our results over existing results is that the new bounds can be always obtained if the stabilizing solution exists, whereas all existing bounds might not be computed because they require other conditions additional to the existence condition.

A state-discretization approach [11], which was introduced for stability of constant delayed systems, will be extended to time-varying delayed systems. The states not only in constructing the Lyapunov-Krasovskii functional but also in designing the integral inequality technique [12] will be discretized. Based on the discretized-state, [9],[17] 's piecewise analysis method will be applied to confirm the system stability in whole delay bound. Numerical examples show that the results obtained by this criterion improve the allowable delay bounds over the existing results in the literature.