Mean stability and stabilization of positive linear systems subject to mode-dependent Poisson jumps

This paper deals with the class of positive linear systems subject to Poisson jumps. The random jumps are described by an exponential distribution with mode-dependent parameter. Contrary to classical Markov Jump Linear Systems, no probabilistic information on the sequence of modes is assumed to be available. Mean stability of this class of systems is analyzed, showing that it is equivalent to stability under arbitrary switching of a suitably defined deterministic switching system. Sufficient conditions for mean stability are worked out by relying on common copositive (linear or quadratic) Lyapunov functions. Similar conditions are derived for designing a state-feedback control law guaranteeing closed-loop mean stability and positivity.