Stochastic finite-time stability and stabilisation of semi-Markovian jump linear systems with generally uncertain transition rates

This paper investigates the stochastic finite-time stability and the state feedback controller design for the linear semi-Markovian jump systems with generally uncertain transition rates. Firstly, sufficient condition is established by using a stochastic Lyapunov functional. Secondly, based on the linear matrix inequality condition, the state feedback controller is obtained to guarantee the finite-time stabilisation. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.