In this paper, we study the almost sure-stability and delta-moment sta
bility of discrete-time jump linear systems with a finite state form p
rocess. Criteria for almost sure and delta-moment stability, which are
necessary and sufficient conditions for (scalar) one-dimensional syst
ems, are derived. The relationship between almost sure and delta-momen
t stability for (scalar) one-dimensional systems is also presented. If
the system matrices commute, necessary and sufficient conditions for
almost sure stability are obtained.