Lyapunov Matrices for the Stability Analysis of a Multiple Distributed Time-Delay System with Piecewise-Function Kernel

We present the construction of a Lyapunov matrix for a multiple distributed time-delay system with piecewise-function kernel. The construction of this matrix is reduced to the computation of the solutions of a delay free system of matrix equations. The Lyapunov matrix also allows us to perform a stability analysis in the time-domain. This analysis consists in the positivity test of a matrix composed of Lyapunov matrices. Two illustrative examples show the results of the approach.