Upper bounds of the continuous ARE solution

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