Stability analysis of random systems with Markovian switching and its application

This paper aims to study a class of Markovian switching random systems with stochastic processes whose α-order moments (α>1) are finite. Compared with the existing results, the existence and uniqueness of solutions to random systems with Markovian switching is not given as a priori information but guaranteed under some general conditions. The corresponding criteria on noise-to-state stability and boundedness are presented by employing the Lyapunov method. Finally, based on the derived results, a design procedure of state-feedback tracking control is proposed, which is illustrated through two examples.