Hybrid positive systems subject to Markovian switching

This paper deals with the stability analysis, as well the synthesis design for positive linear systems subject to random Markovian switching. The proposed stabilizing control laws are required to preserve the positivity of the system, that is the state variable take nonnegative values whenever the initial state is nonnegative. For this kind of systems, different notions of stochastic stability are defined and it is shown that they are all equivalent. Moreover, all the provided conditions are necessary and sufficient. Beside that, it is shown how the proposed approach can handle the case when the Markovian switching process is not exactly know.