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In this contribution two procedures for the computation of Lyapunov matrices of neutral type time delay systems are presented. The first one is a semi-analytic method, that consists in solving a two points boundary value problem for a delay free system. The second one is a piece-wise linear approximation of the Lyapunov matrix. An algorithm for the estimation of the error based on Lyapunov-Krasovskii functionals is also proposed. [ABSTRACT FROM AUTHOR]

A new method that reveals conditions under which the characteristic function of a linear time delay system has a root s0 such that –s0 is also a root of the function is presented. The method is based on some recent results on the computation of the Lyapunov matrices for time delay systems. A general class of linear systems with distributed delays is studied. A number of examples are given to illustrate the approach and to show its strength. [ABSTRACT FROM AUTHOR]