Approximations of Lyapunov-Krasovskii functionals of complete type with a prescribed cross term in the derivative

Sufficients conditions for the stability analysis of linear single delay systems are given. The results is achieved within the Lyapunov-Krasovskii framework through a piece-wise linear approximation of functional of complete type, whose derivative includes a cross term. The conditions are stated in terms of linear matrix inequalities whose size depends on the precision of the approximation