Mean square stability of linear systems with Poisson jumps

This paper deals with the class of linear systems subject to Poisson jumps, where the dwel-ltime between jumps is described by an exponential distribution with mode-dependent parameter. No probabilistic information on the sequence of modes is assumed available. This model can be viewed as an uncertain Markov Jump Linear System (MJLS) with a transition rate matrix belonging to a polytope. Thanks to this interpretation, we show that mean square stability is equivalent to stability under arbitrary switching of a deterministic system. This allows one to derive sufficient conditions for mean square stability based on common Lyapunov functions, easily testable via semidefinite programming. Conservatism of the proposed conditions is discussed along with the relative implications among them.