  We describe a new class of positive linear discrete-time switching systems
for which the problems of stability or stabilizability can be resolved
constructively. This class generalizes the class of systems with independently
switching state vector components. The distinctive feature of this class is
that, for any system from this class, its components or blocks can be
arbitrarily connected in parallel or in series without loss of the
`constructive resolvability' property. It is shown also that, for such systems,
it is possible to build constructively the individual positive trajectories
with the greatest or the lowest rate of convergence to the zero.
