  Several results regarding the stability and the stabilization of linear
impulsive positive systems under arbitrary, constant, minimum, maximum and
range dwell-time are obtained. The proposed stability conditions characterize
the pointwise decrease of a linear copositive Lyapunov function and are
formulated in terms of finite-dimensional or semi-infinite linear programs. To
be applicable to uncertain systems and to control design, a lifting approach
introducing a clock-variable is then considered in order to make the conditions
affine in the matrices of the system. The resulting stability and stabilization
conditions are stated as infinite-dimensional linear programs for which three
asymptotically exact computational methods are proposed and compared with each
other on numerical examples. Similar results are then obtained for linear
positive switched systems by exploiting the possibility of reformulating a
switched system as an impulsive system. Some existing stability conditions are
retrieved and extended to stabilization using the proposed lifting approach.
Several examples are finally given for illustration.
