A Note on Relationship Between Two Classes of Integral Inequalities

This technical note firstly introduces two classes of integral inequalities with and without free matrices, respectively, and points out that they, although in different forms, are actually equivalent in the sense of conservatism, i.e., the two corresponding ones produce the same tight upper bounds. Secondly, the relationship between the method of integral inequalities with free matrices and the free-weighting matrix technique is intensively investigated. It is shown that these two different methods are actually equivalent in assessing the stability of time-delay systems.