  The Wigner-Smith (WS) time delay matrix relates a system's scattering matrix
to its frequency derivative and gives rise to so-called WS modes that
experience well-defined group delays when interacting with the system. For
systems composed of nondispersive and lossless materials, the WS time delay
matrix previously was shown to consist of volume integrals of energy-like
densities plus correction terms that account for the guiding, scattering, or
radiating characteristics of the system. This study extends the use of the WS
time delay matrix to systems composed of dispersive and lossy materials.
Specifically, it shows that such systems' WS time delay matrix can be expressed
by augmenting the previously derived expressions with terms that account for
the dispersive and lossy nature of the system, followed by a transformation
that disentangles effects of losses from time delays. Analytical and numerical
examples demonstrate the new formulation once again allows for the construction
of frequency stable WS modes that experience well-defined group delays upon
interacting with a system.
