Abstract
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.
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