Finite-time stability for positive Markovian jump systems with partly known transition rates

The paper is concerned with finite-time stability for positive Markovian jump systems with partly known transition rates. First, by constructing appropriate linear co-positive Lyapunov-Krasovskii function, sufficient conditions for finite-time stability of underlying system are given. Then, in virtue of the results obtained, an effective method is proposed for the construction of the state feedback controller. All the proposed conditions are derived to ensure the closed-loop Markovian jump system positive and finite-time stability in linear programming. Finally, an example is given to demonstrate the validity of the main results.