Polynomial approximations of the Lyapunov matrix of a class of time delay systems

A polynomial approximation of the Lyapunov matrix appearing in the complete type Lyapunov Krasovskii functionals associated to a class of retarded time delay systems is proposed. The results are concordant with the available semi-analytic solution. The comparison of the approximation error with that of the piecewise linear approximation previously introduced in the literature shows a significant improvement.