Almost sure stabilization of positive systems under asynchronous Markovian switching

In this paper, a new Lyapunov method is used to study the almost sure stabilization of positive Markovian jump linear systems (PMJLSs) under asynchronous Markovian switching. This method is established by a composite Lyapunov function. Moreover, the almost surely exponential stability criterion of the closed-loop PMJLSs under asynchronous condition is presented, and a controller is designed by means of bilinear matrix inequalities (BMIs). The quantitative relationship among the magnitude, stationary distribution and Markov chain generator of the detected switch signal delay can be given by the obtained results. Finally, a simulation example is given to verify the theoretical results.