The paper deals with the problem of delay‐dependent output feedback L1 control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates. First, by constructing an appropriate co‐positive type Lyapunov function, sufficient conditions for stochastic stability and L1‐gain performance of the open‐loop system are developed. Then, an effective method is proposed to construct the output feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, a numerical example is given to illustrate the validity of the main results.
