  LPV systems with piecewise constant parameters subject to spontaneous
Poissonian jumps are a class of systems that does not seem to have been
thoroughly considered in the literature. We partially fill this gap here by
providing sufficient stability and performance analysis conditions stated in
terms of infinite-dimensional LMI problems that can be solved using sum of
squares programming. A particularity of the obtained conditions lies in the
presence of an integral term leading to some technical difficulties when
attempting to obtain convex conditions for the design of a gain-scheduled
state-feedback controller. This difficulty is circumvented by relying on a
recent result for time-delay systems analysis and an equivalent integral-free
LMI condition is obtained. The approach is illustrated through several
examples.
