Stochastic stability and stabilization for positive Markov jump systems with distributed time delay and incomplete known transition rates

This paper studies the problem of stochastic stability and stabilization for positive Markov jump systems with distributed time delay and incomplete known transition rates. By using delay partitioning technique, a new form of Lyapunov functional is constructed and a stochastic stability criterion is formulated for positive Markov jump systems with fully known transition rates. Based on this, the case of incomplete known transition rates is discussed. Then a state feedback controller is designed to guarantee the corresponding closed-loop system positive and stochastically stable. The results in this paper are expressed in the form of linear programming problems, and can be easily solved by standard software.