  In this paper, new weighted integral inequalities (WIIs) are first derived by
refining the Jensen single and double inequalities. It is shown that the newly
derived inequalities in this paper encompass both the Jensen inequality and its
most recent improvements based on Wirtinger integral inequality. The potential
capability of the proposed WIIs is demonstrated through applications in
exponential stability analysis for some classes of time-delay systems in the
framework of linear matrix inequalities (LMIs). The effectiveness and least
conservativeness of the derived stability conditions using WIIs are shown by
various numerical examples.
