Upper bounds of the continuous ARE solution

Abstract

In this paper, we provide a bound of the continuous ARE solution in terms of a matrix associated with Lvapunov 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 thf 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.