In this paper, the problem of robust stability for a class of time-delay systems
is investigated. The uncertainties possessed in the systems are assumed to be time invariant
and belong to a convex bounded polytopic domain. For comparison, both single
polyhedral and double polyhedral Lyapunov functionals are defined according to the form
of a Lyapunov–Krasovskii functional. Robust stability results are obtained by using the
double polyhedral Lyapunov functional approach. Also, for a known convex uncertainty
subdomain, two equivalent conditions are presented. All established stability conditions are
expressed in terms of linear matrix inequalities. Numerical examples are given to illustrate
the effectiveness and usefulness of the main theoretic results.