  This paper is devoted to stability analysis of continuous-time delay systems
based on a set of Lyapunov-Krasovskii functionals. New multiple integral
inequalities are derived that involve the famous Jensen's and Wirtinger's
inequalities, as well as the recently presented Bessel-Legendre inequalities of
A. Seuret and F. Gouaisbaut, (2015) and the Wirtinger-based multiple-integral
inequalities of M. Park et al. (2015) and T.H. Lee et al. (2015).
  The present paper aims at showing that the proposed set of sufficient
stability conditions can be arranged into a bidirectional hierarchy of LMIs
establishing a rigorous theoretical basis for comparison of conservatism of the
investigated methods. Numerical examples illustrate the efficiency of the
method.
