  In discrete-time linear dynamical systems (LDSs), a linear map is repeatedly
applied to an initial vector yielding a sequence of vectors called the orbit of
the system. A weight function assigning weights to the points in the orbit can
be used to model quantitative aspects, such as resource consumption, of a
system modelled by an LDS. This paper addresses the problems to compute the
mean payoff, the total accumulated weight, and the discounted accumulated
weight of the orbit under continuous weight functions and polynomial weight
functions as a special case. Besides general LDSs, the special cases of
stochastic LDSs and of LDSs with bounded orbits are considered. Furthermore,
the problem of deciding whether an energy constraint is satisfied by the
weighted orbit, i.e., whether the accumulated weight never drops below a given
bound, is analysed.
