Lyapunov Matrices for Integral Delay Systems with Piecewise Constant Kernel

Integral delay systems with piecewise constant kernel are studied. The delay Lyapunov matrix for the case of commensurate delays is computed by solving an auxiliary boundary value problem of delay-free linear matrix differential equations. The relation between the solution of the auxiliary system and the delay Lyapunov matrix is discussed. It is also shown that if the integral delay system satisfies the Lyapunov condition, then the delay Lyapunov matrix is unique.