Lyapunov matrices for time-delay systems

The construction of complete-type Lyapunov-Krasovki˘ i functionals for a linear time-invariant delay system depends on so-called delay Lyapunov matrices which satisfy a matrix delay equation with additional boundary conditions. We study existence and uniqueness issues for these delay Lyapunov matrices. © 2006 Elsevier B.V. All rights reserved.